Answer
$$y'=-2\cot(\sin\theta)\csc^2(\sin\theta)\cos\theta$$
Work Step by Step
$$y'=(\cot^2(\sin\theta))'=2\cot(\sin\theta)(\cot(\sin\theta))'=
2\cot(\sin\theta)(-\frac{1}{\sin^2(\sin\theta)})(\sin\theta)'=-2\cot(\sin\theta)\csc^2(\sin\theta)\cos\theta$$
