# Solve it in Friday 13th - part 1

Geometry Level 5

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

If the trigonometric expression above can be expressed as $$\dfrac{\sqrt{\alpha}-\beta}{\gamma}$$ for positive integers $$\alpha,\beta,\gamma$$ with where $$\alpha$$ doesn't have squared factors and $$\text{gcd}(\beta,\gamma)=1$$, find $$\alpha+\beta+\gamma$$.

See Part 2 and Part 3.

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