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:

\intcos²(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\Thetacos(2\Theta)sin(2\Theta)d\Theta, and then putting it into the form \intUdV=UV-\intVdU, 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