I'm having difficulty solving the following equation which helps locate the angles in young's double slit experiment. Currently I'm using a graphical method.

The equation is:

$\displaystyle C^2 - b^2 - a^2$ = $\displaystyle \frac{a}{\tan^2(\theta)} + \frac{2aC}{\sin(\theta)} - \frac{2ba}{\tan(\theta)} - \frac{a^2}{\sin^2(\theta)}$

a, b and C are constants.

I tried expressing $\displaystyle {\tan(\theta)}$ in terms of $\displaystyle {\sin(\theta)}$.

However,$\displaystyle {\tan(\theta)}$ = ±$\displaystyle \frac{\sin(\theta)}{\sqrt{\1-sin^2(\theta)}}$

And I'm not sure how to deal with the ±, given that I would like tomake θ the subject, where 0 < θ < $\displaystyle \pi$.