Trigonometry! #38

Geometry Level 4

Let $a$ , $b$ and $c$ be positive real numbers such that $\theta=\tan^{-1} \sqrt{\frac {a(a+b+c)}{bc}} + \tan^{-1} \sqrt{\frac {b(a+b+c)}{ca}} + \tan^{-1} \sqrt{\frac {c(a+b+c)}{ab}}$ Then find the value of $\tan \theta$ .

This problem is part of the set Trigonometry.