Waiting for 2016 - 3

Geometry Level 5

S=cos(2π13)+cos(6π13)+cos(8π13)\large \mathcal{S} = \cos \left(\dfrac{2 \pi}{13} \right) + \cos \left(\dfrac{6 \pi}{13} \right) + \cos \left(\dfrac{8 \pi}{13} \right)

If the value of S\mathcal{S} is of the form abc\dfrac{\sqrt{a} - b}{c}, where a,ba,b and cc are positive integers with aa square free, find the value of a+b+ca+b+c.

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