Start with the identities for `cos2theta` :
With some algebra you can find reduction formulas for higher powers. Please see reference for these formulas.
** I find it far more useful to be able to derive the formulas than to just memorize them. You really only need to memorize a few identities, and then know how to manipulate them. Of course, in a school setting it helps to know formulas, but in the long run you will find it far more helpful to understand how to get the formulas on your own.