Is the following trigonometric equation solvable? I have the following equation, and I want to solve for $\theta$ :
$$f(x,y,\theta) = \frac{x \cos(\theta) - y \sin(\theta)}{x \sin(\theta) + y \cos(\theta)}$$
It seems to me this equation should be easily solvable given known $x$ and $y$, however I cannot find it. Any help/hints?
EDIT: There was an error in my equation. I also must add that I know the value of $f$. Currently working on it with the tip given by Chandrasekhar. 
It is important to note that $\theta$ and $x$, $y$ are not related. Yes it can be seen as a rotation... (or the division of the two terms from a rotation).

Let $x = r \sin(\alpha)$ and $y = -r \cos(\alpha)$. Then
$$
   f(x,y,\theta) = \frac{ \sin(\alpha) \cos(\theta) +  \cos(\alpha) \sin(\theta)}{ \sin(\alpha) \sin(\theta) - \cos(\alpha) \cos(\theta)} = \frac{ \sin( \alpha+\theta )}{ \cos(\alpha+\theta)} = \tan(\alpha+\theta) 
$$
