Soviet Russian Cosine #1

Geometry Level 3

If the exact value of \(\displaystyle\cos\frac{\pi}{5} - \cos\frac{2\pi}{5} \) can be represented in the form \(\displaystyle\frac{a\sqrt{b}}{c}\), and \( gcd(a, b, c) = 1\), then find \(a+b+c\).

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