The method that pickslides used was very neat, Tweety.
He used the same identity at each step.
You may see the identity written as
Rearranging this, we get
so
He simply used this, by letting A=2x to get cos4x
and the powers of x follow.
I started with the powers and worked back, eventually using that identity,
but i also used
in writing
The other identity i used is