Hi, I'm struggling to understand how to prove this:

(sin^4) T = ( 3 - 4 cos 2 T + cos 4 T ) / 8

(where T is theta)

I start on the left side and "break" this up into a square:

( sin^2 T) ^ 2

From here, my book does the following:

( 1 - cos 2 T / 2 ) ^ 2

Why?

I know sin^2 is also = 1 - cos ^ 2

How do I know to use the double angle identity?? It doesn't seem to apply if I'm just working with sin^2 T?

Thanks!