Soviet Russian Cosine #2

Geometry Level 3

If the exact value of \(\displaystyle\cos\frac{2\pi}{7}+\cos\frac{4\pi}{7}+\cos\frac{6\pi}{7}\) 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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