Can you rearrange an equation like what i have done?
$\displaystyle a^2cos^2\theta a^2sin^2\theta d\theta = a^4cos^2\theta sin^2\theta d\theta$
as long as each $\displaystyle a$ is a distinct constant factor, you sure can.
you can also do this ...
$\displaystyle a^4\cos^2{\theta} \sin^2{\theta} \, d\theta =$
$\displaystyle \frac{a^4}{4} \sin^2(2\theta) \, d\theta =$
$\displaystyle \frac{a^4}{8}[1 - \cos(4\theta)] \, d\theta$