Trigone Mania

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

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