$\sin\left (\frac{2π}{7} \right )+\sin\left (\frac{4π}{7} \right )+\sin \left(\frac{8π}{7} \right )$

The value of the expression above can be expressed in the form $a+\frac{\sqrt{b}}{c}$ where $a,b,c$ are whole numbers with $b$ is square-free.

Find $a+b+c$.

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