A geometry problem by Mateus Gomes

Geometry Level 4

sin(2π7)+sin(4π7)+sin(8π7)\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 AB \dfrac {\sqrt A}B , where AA and BB are positive integers with AA square-free, find A+BA+B.

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