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.

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