Trigonometry! 12

Geometry Level 3

Given that 0<α,β<π40<\alpha,\beta<\dfrac {\pi}{4} such that cos(α+β)=45 \cos (\alpha + \beta) = \dfrac {4}{5} and sin(αβ)=513\sin (\alpha - \beta) = \dfrac {5}{13} holds true, find tan2α\tan 2\alpha.

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