Subjected to His Will

Subjected to His Will is a companion quest for Cole in Dragon Age: Inquisition.

Solas says that finding an Amulet of the Unbound will prevent Venatori mages from binding Cole

Acquisition

Speak to Cole in the Herald's Rest after completing Here Lies the Abyss.

Walkthrough

Complete the cutscene with Solas to further investigate Cole's fear of being bound against his will like the demons at Adamant. At the end of the scene, the Inquisitor should agree to pursue the Rivaini Amulet.
Complete the war table operation, Obtain Amulet for Cole and you are granted the Amulet of the Unbound

Note: Though the Inquisitor is rewarded with the amulet for the operation, it does not appear in the player inventory.

Speak to Cole again and select the special dialogue option "Give Cole the amulet." Doing so triggers another cutscene, during which Solas attempts to charge the amulet with protective magic, but fails. Another cutscene triggers which explains how Cole came to be and why the amulet did not work.
Toward the end of the scene, you need to make an important decision about Cole's future.

Rewards

1934 XP
400 Influence
3 Power

Approval

At Skyhold with Cole, Solas, and Varric.

[Give Cole the amulet] - Cole Approves

Solas: It is simple enough. You put it on, I charge it with magic, and you should be protected.

All right, if Cole is sure. - Solas Slightly Approves, Cole Slightly Approves
You think this will work?
Do it. - Solas Slightly Disapproves, Cole Slightly Disapproves

Varric: Something like Cole not being a demon?

Cole is a demon. - Solas Slightly Approves, Varric Slightly Disapproves
I don't know what Cole is.
Maybe Varric is right. - Solas Slightly Disapproves

Cole: There. That way.

No approval changes.

Varric: But he came into this world to be a person. Let him be one.

I care about results. - Solas Slightly Disapproves
I agree, Varric. - Varric Slightly Approves
No, Solas is right. - Solas Slightly Approves

Confrontation at Redcliffe.

Cole: He killed me. He killed me. That's why it doesn't work. He killed me, and I have to kill him back!

Cole, wait. - Varric Slightly Approves

Let me kill him. I need to... I need to.

Cole must forgive this. (Cole becomes more like a spirit) - Solas Greatly Approves, Varric Disapproves, Cole Greatly Approves
Cole needs to grow. (Cole becomes more human) - Solas Disapproves, Varric Greatly Approves, Cole Greatly Approves

Returning to Skyhold.

Cole: It still hurts. When do I stop hurting?

We'll help. - Varric Approves
I have no idea.
You don't. - Varric Slightly Disapproves

Cole: Nonsense words, like Bartrand at the end. "Just need to hear the song again. Just for a minute." I'm all right, Varric.

Are you happy, Cole?
I'm with Varric on this. - Varric Slightly Approves
I can't understand him.

Notes

Unused banter dialogue between Cole and Blackwall implies that it was at one time possible to allow Cole to kill the templar.

Bugs

There is a known Xbox 360 xbox360 console crash when trying to deliver the amulet to Cole. If this happens, do as follows: Go to the top floor of the tavern but do not approach Cole, instead immediately exit the door on the left. Once you have gone through the door into the adjacent room turn back around and take a small step back into the tavern. When back inside, the far wall directly in front of you will turn red in color as if a lamp has been lit. Once this happens you will be safe to approach Cole and continue his quest. If you've taken too many steps back into the tavern when the lighting occurs, the console will freeze.
If you are not experiencing the red wall, another potential solution is waiting for an Approval change for Cole. As long as you don't load a save file between the Approval change and attempting to give Cole the amulet, it should work. Saving the game does not seem to affect this process. A specific example that has been tested to work is to Sit in Judgement for Grand Duchess Florianne de Chalons. Choosing the Encloister, Recruitment, or Farm Work options result in Cole Approves or Cole Disapproves. If you head straight to Cole after choosing any of the options that affect Cole's Approval, the game shouldn't crash, though this is not any more a guarantee than the above method. This also works for Slight Approval changes and Great Approval changes, both negative and positive, both within Skyhold and without. Slight Approval changes seem to still occasionally result in a crash, but in general work after one or two attempts.
Alternatively, you may also wait until completing What Pride Had Wrought. A new cut scene will trigger about the amulet if you talk to Cole, after which you may talk to him normally again.