Answer
$$\rho=2 \cot\phi \csc\phi \csc 2\theta.$$
Work Step by Step
We have
$$z=xy\Longrightarrow \rho \cos\phi=\rho^2\sin^2\phi\cos\theta\sin\theta\\
=\frac{1}{2}\rho^2\sin^2\phi \sin2\theta .$$
That is $$\rho=2 \cot\phi \csc\phi \csc 2\theta.$$
