# Trigone Mania

Geometry Level 3

$\tan^{-1}\left(\dfrac{2\cos\dfrac{\pi}{18}-\cos\dfrac{5\pi}{18}}{\sin\dfrac{7\pi}{18}-\cos\dfrac{4\pi}{9}}\right)$

If the expression above can be written as $$\dfrac{A\pi}{B}$$, where $$A$$ and $$B$$ are coprime positive integers, find $$A+B$$.

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