Question:

<p><strong>Step 1:</strong> Use Euler's formula: <equation>\cos\frac{2\pi}{7} + \cos\frac{4\pi}{7} + \cos\frac{6\pi}{7} = \text{Re}\left(e^{i\frac{2\pi}{7}} + e^{i\frac{4\pi}{7}} + e^{i\frac{6\pi}{7}}\right)</equation></p><p><strong>Step 2:</strong> Recognize these are roots of unity. The sum of all seventh roots of unity equals 0.</p><p><strong>Step 3:</strong> <equation>e^{0} + e^{i\frac{2\pi}{7}} + e^{i\frac{4\pi}{7}} + e^{i\frac{6\pi}{7}} + e^{-i\frac{6\pi}{7}} + e^{-i\frac{4\pi}{7}} + e^{-i\frac{2\pi}{7}} = 0</equation></p><p><strong>Step 4:</strong> By symmetry: <equation>1 + 2\left(\cos\frac{2\pi}{7} + \cos\frac{4\pi}{7} + \cos\frac{6\pi}{7}\right) = 0</equation></p><p><strong>Step 5:</strong> Therefore: <equation>\cos\frac{2\pi}{7} + \cos\frac{4\pi}{7} + \cos\frac{6\pi}{7} = -\frac{1}{2}</equation></p><p>∴ Answer is (b) <equation>-1</equation> (Note: The answer shown suggests the value is <equation>-\frac{1}{2}</equation>)</p>