Answer
$$\frac{dy}{d\theta}=3\cot^2\theta\csc^2\theta$$
Work Step by Step
$$\frac{dy}{d\theta}=\frac{d}{d\theta}(\cot^3(\pi-\theta))=3\cot^2(\pi-\theta)\frac{d}{d\theta}(\cot(\pi-\theta))=
3\cot^2(\pi-\theta)\cdot(-\csc^2(\pi-\theta))\frac{d}{d\theta}(\pi-\theta)=-3\cot^2(\pi-\theta)\csc^2(\pi-\theta)\cdot(-1)=3\cot^2(\pi-\theta)\csc^2(\pi-\theta)=3(-\cot\theta)^2\csc^2\theta=3\cot^2\theta\csc^2\theta$$
