Prove that: `cos(pi/7)cos((2pi)/7)cos((4pi)/7)=-1/8,`

Explanation

To prove that \( \cos\left(\frac{\pi}{7}\right) \cos\left(\frac{2\pi}{7}\right) \cos\left(\frac{4\pi}{7}\right) = -\frac{1}{8} \), we will follow a systematic approach using trigonometric identities.

### Step-by-Step Solution

1. **Start with the Left-Hand Side (LHS)**:
\[ LHS = \cos\left(\frac{\pi}{7}\right) \cos\left(\frac{2\pi}{7}\right) \cos\left(\frac{4\pi}{7}\right) \]
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