# A geometry problem by Mateus Gomes

Geometry Level 4

$\sin \left(\dfrac{2\pi}{7}\right)+\sin \left(\dfrac{4\pi}{7}\right)+\sin \left(\dfrac{8\pi}{7}\right)$

If the value of the expression above is equal to $\dfrac {\sqrt A}B$, where $A$ and $B$ are positive integers with $A$ square-free, find $A+B$.

×