Solving a Tricky Integral: Help with Double Integrals in Polar Coordinates

[KaiserBrandon]

Homework Statement

I can't seem to figure out how to solve this integral:

$$\int$$cos²(2$$\Theta$$)d$$\Theta$$

Homework Equations

none

The Attempt at a Solution

I tried doing integration by parts by first letting v=d$$\Theta$$ and dV=$$\Theta$$, and U=cos²(2$$\Theta$$) and dU=-4$$\Theta$$cos(2$$\Theta$$)sin(2$$\Theta$$)d$$\Theta$$, and then putting it into the form $$\int$$UdV=UV-$$\int$$VdU, but that didn't really take me anywhere. Is there another way I should try to solve this integral? This is my fourth university calc class, and the full question is double integrals with polar coordinates, so I probably learned how to solve these types of integrals somewhere down the road, I just can't seem to remember. Thanks in advance

 

[Mark44]

Hint: cos²(t) = (cos(2t) + 1)/2