A geometry problem by Jose Sacramento

Geometry Level 4

\[\large \frac{\cos\left( \frac{2\pi}7 \right) + \cos\left( \frac{4\pi}7 \right) + \cos\left( \frac{6\pi}7 \right) }{\cos\left( \frac{\pi}7 \right) \times \cos\left( \frac{3\pi}7 \right) \times \cos\left( \frac{5\pi}7 \right)} = \, ? \]

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