Well, the problem is:

$\displaystyle sin4t = 4 sint cost(1-2sin^2t)$

For some reason I always get confused in verifying the identity ><;. Now, I tried various forms of doing it like changing sin4t to sin(2t+2t) but it just ends up getting jumbled up. Any help on how to not get so confused with "Verify the identity" problems or just pushing me in the right direction to solve this one would be appreciated.