Sine Summation

Geometry Level 4

\[ \large \sin \dfrac{2\pi }7 + \sin \dfrac{4\pi }7 + \sin \dfrac{8\pi }7 \]

If the value of the expression above can be expressed as \( \dfrac {\sqrt a}b \), where \(a\) and \(b\) are coprime positive integers, find \(a+b\).

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