Trigonometry! #62

Geometry Level 4

Find the value of \[ \tan \left( 2\tan^{-1} \left(\frac {1}{5} \right) - \frac {\pi}{4} \right) \]

Express your answer in the form of \(-\frac {a}{b}\) where \(a\) and \(b\) are positive coprime integers, and enter the value of \(a+b\).

This problem is part of the set Trigonometry.

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