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