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Let aaa, bbb and ccc be positive real numbers such that θ=tan−1a(a+b+c)bc+tan−1b(a+b+c)ca+tan−1c(a+b+c)ab\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}}θ=tan−1bca(a+b+c)+tan−1cab(a+b+c)+tan−1abc(a+b+c) Then find the value of tanθ\tan \thetatanθ.
This problem is part of the set Trigonometry.
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