After it's claptoned hold the end with smooth jaw pliers and slowly twist in the opposite direction to remove the twist.
Or just untwist it with nylon pliers as you wrap it. Whenever I'm coiling up a build whether it be fused claps or tricore aliens they usually have multiple twists in the wire (not the cores bunching up, but the wires kind of all moving with each other at the same time). When you go to coil it up, just pull tension at the end of the stick and kind of lean it whichever way you want to flatten out. The twists should come out normally when you go to coil it up, there's no need to go over the entire finished product to get rid of a couple twists.
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