Complenometry

Geometry Level 3

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

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 \(a+b+c\).

This is similar to Know Some Trigonometry
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