Area of polar curves

I am having trouble finding the area between 2 polar curves..... I have the procedure down, but the bounds are throwing me off. Any help with understanding how to bound would be great appreciated!

I have attatched one problem that I am having hard time with and the work I have done. I know that I am doing something wrong because I am getting a negative number for an area (which shouldn't be).

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$$\frac{A}{2}=\frac{1}{2}\int_{\frac{\pi}{3}}^{\pi}(1+\cos(\theta))^2 d\theta - \frac{1}{2}\int_{\frac{\pi}{3}}^{\frac{\pi}{2}}(3\cos(\theta))^2 d\theta$$