How can I solve for a single variable which occurs in multiple trigonometric functions in an equation? This is a pretty dumb question, but it's been a while since I had to do math like this and it's escaping me at the moment (actually, I'm not sure I ever knew how to do this. I remember the basic trigonometric identities, but not anything like this).
I have a simple equation of one unknown, but the unknown occurs twice in different trigonometric functions and I'm not sure how to combine the two. I want to simply solve for $\theta$ in the following equation, where $a$ and $b$ are constants.
$a=\tan(\theta) - \frac{b}{\cos^2\theta}$
How can I reduce this into a single expression so that I can solve for $\theta$ given any $a$ and $b$?
(I'm only interested in real solutions and, in practice (this is used to calculate the incidence angle for a projectile such that it will pass through a certain point), it should always have a real solution, but an elegant method of checking that it doesn't would not go unappreciated.)

Based on Braindead's hint I reduced the equation to:
$0=(b-a)+\tan(\theta)+b\tan^2(\theta)$
I can now solve for $\tan(\theta)$ using the quadratic equation, which gets me what I'm after. Is this the solution others were hinting towards? It seems like there would be a way to do it as a single trigonometric operation, but maybe not.

You can write $\tan(\theta)=\frac{\sin(\theta)}{\cos(\theta)}=\frac{\sqrt{1-\cos^2(\theta)}}{\cos(\theta)}$ which gets everything in terms of $\cos(\theta)$ but you may not like the degree of the result when you get rid of the radical.
