Trigonometry! 12

Geometry Level 3

Given that $$0<\alpha,\beta<\dfrac {\pi}{4}$$ such that $$\cos (\alpha + \beta) = \dfrac {4}{5}$$ and $$\sin (\alpha - \beta) = \dfrac {5}{13}$$ holds true, find $$\tan 2\alpha$$.

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