TITLE: How to solve $A\tan\theta-B\sin\theta=1$
QUESTION [6 upvotes]: I was wondering if it is possible to solve
$$A\tan\theta-B\sin\theta=1$$
for $\theta$, where $A>0,B>0$ are real constants. 
For sure this can be straightforwardly implemented numerically, but maybe an alternative exists :)...

REPLY [2 votes]: Like any other quartic equation, there is a classical way to solve it explicitly in terms of radicals; but this is generally very messy. It is practically much easier, and no less accurate in the final analysis, to solve it by a numerical method such as Newton--Raphson.