# Waiting for 2016 - 3

Geometry Level 5

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

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

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