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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