Find the area of the region described

The region enclosed by the inner loop of the limacon r=1+2cosθ

http://img530.imageshack.us/img530/4039/66298286hz2.png

This is the answer

I do not know how to find limits of integration is from 2pi/3 to pi/3

Not only this problem, Im confusing in all the same problem

Please explain to me not only in this problem, explain more generally

Thank you