Solve it in Friday 13th - part 2

Geometry Level 4

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

If the trigonometric expression above can be expressed as \(-\dfrac{\alpha}{\beta}\) for coprime positive integers \(\alpha\) and \(\beta\), find the value of \(\alpha+\beta\).

See Part 1 and Part 3.

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