I am working on a problem and obtained the following equation:
$$ \tan \beta = \frac{\lambda - \cos \theta}{\sin \theta} \Leftrightarrow \tan \beta = \lambda\cdot \csc \theta-\cot \theta$$
Where $\lambda$ is a constant.
Is it possible to simplify the right hand side term into a single trig function? My goal is to have an equation of the form $$\theta = f(\beta)$$
I have tried different trig identities but I only end up making it worse.
Any help is appreciated.
Thank you!