What is the functional inverse of $f(\theta) = \sin\theta\sqrt{\tan\theta}$? Or, equivalently, what is the inverse of 
$$f(\theta)=\sin^2\,\theta\tan\,\theta=\frac{\sin^3\,\theta}{\cos\,\theta}$$

It comes from a physics setup involving two equivalently massed and charged pith balls separated by a certain distance, and the equation simplifies to $q = 4L\sin\theta\sqrt{\pi\epsilon\_0mg\tan{\theta}}$, where $\pi$, $g$, and $\epsilon\_0$ are the obvious physical constants and $L$ and $m$ will be fixed. The question asked for $\theta$ in terms of $q$, however, so I'm wondering if there is a way to rearrange this. I can't seem to find anything on the internet, and Wolfram refuses to reveal the steps for its complex rearranged formula.