Simplifying an equation

Can anyone shed light on how the following simplification was achieved?

I had: $\displaystyle 4a^2 w^2 (coswt + cos2wt)^2 + 4a^2 w^2 (sin2wt - sinwt)^2 $

Which became:

$\displaystyle 8a^2 w^2 (1 + cos3wt) $

I expect there is a trig identity required but my mind is blank, help!

To simplify things, look at $\displaystyle (\cos(2\theta) + \cos(\theta))^2 + (\sin(2\theta) - \sin(\theta))^2 $

=$\displaystyle \cos^2(2\theta) +2\cos(2\theta)\cos(\theta) + \cos^2(\theta) + \sin^2(2\theta) -2\sin(2\theta)\sin(\theta) +\sin^2(\theta) $

$\displaystyle =2 + 2(\cos(2\theta)\cos(\theta)-\sin(2\theta)\sin(\theta))$

$\displaystyle =2 + 2\cos(2\theta+\theta)$

Got it, thank you very much.