Cunning ploy

Geometry Level 4

If the exact value of \( \tan { \left( \frac { 2\pi }{ 13 } \right) } +4\sin { \left( \frac { 6\pi }{ 13 } \right) } \) is of the form \( \sqrt { A+2\sqrt { B } } \) where \(A\) and \(B\) are positive integers, find the value of \(A+B\).

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