Consider the following:
Can someone explain why the integration limits for $d \theta$ are between $\frac{3 \pi}{2}$ and $2\pi$?
Surely it should be between $\pi$ and $2\pi$??
Also why are the $r$ limits not between 0 and 4?
Any help is greatly appreciated!!

HINT (rather than an answer)
So the integration bounds with respect to $\theta$ are $\frac{3\pi}2$ and $2\pi$.
And at a given $\theta$: $0\le r\le 4\cos(\theta).$