Complenometry

Geometry Level 3

sin(2π7)+sin(4π7)+sin(8π7)\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+bca+\frac{\sqrt{b}}{c} where a,b,ca,b,c are whole numbers with bb is square-free.

Find a+b+ca+b+c.

This is similar to Know Some Trigonometry
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