I am having troubles finding the area between two curves from 0 to 2$\displaystyle \pi$:

The inside of r=1+cosθ and the outside of r=2cosθ

Is it possible to simply subtract 2cosθ from 1+cosθ and take the integral of that so it looks like:

$\displaystyle \frac{1}{2} \int_0^{2\pi} (1-cos\theta)^2d\theta $

Thanks ahead of time for the help