The value of $\cos \frac{2\pi}{7} + \cos \frac{4\pi}{7} + \cos \frac{6\pi}{7}$ is:
Step-by-Step Solution
Key Concept: These are the real parts of $e^{2\pi i k/7}$ for $k = 1, 2, 3$. The sum of all 7 complex 7th roots of unity is zero. Use the symmetry $\cos(k \cdot 2\pi/7) = \cos((7 - k) \cdot 2\pi/7)$.
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Correct Answer: (2)