Let $ABC$ be a triangle with $AB=5$, $AC=6$ and $BC=7$ and $O$ be the circle passing through the incenter, circumcenter and orthocenter of $ABC$.
$E$ and $F$ are points on circle $O$ such that $AE$ and $AF$ are tangent to $O$.
$\angle FAE$ is equal to $\displaystyle\frac{a \pi}{b}$ for positive integers $a,b$ with $\mathrm{gcd}(a,b)=1$.
What is $a+b$?
Note: For this problem we are working in Euclidean Geometry.
