Prove that

The first thing to do, obviously, is to find the first derivative, which is

First I tried factoring, then using a couple of trigonometric identities.

None of this, however, gets me any closer to . I differentiated a second time and got

-4(\cos^4x+\sin^4x-24\sin^2x\cos^2x)

I haven't double-checked my math on this last step but I'm pretty sure I'm right, but, regardless, it's not any closer either! So, I ask you, am i doing something wrong or just trying to follow the wrong steps?