The value of `cos(pi/7)+cos((2pi)/7)+cos((3pi)/7)+cos((4pi)/7)+cos((5pi)/7)+cos((6pi)/7)+cos((7pi)/7)` is 1 (b) `-1` (c) 0 (d) none of these

Explanation

To solve the problem, we need to find the value of the expression:

\[ \cos\left(\frac{\pi}{7}\right) + \cos\left(\frac{2\pi}{7}\right) + \cos\left(\frac{3\pi}{7}\right) + \cos\left(\frac{4\pi}{7}\right) + \cos\left(\frac{5\pi}{7}\right) + \cos\left(\frac{6\pi}{7}\right) + \cos\left(\frac{7\pi}{7}\right) \]

### Step 1: Recognize the periodicity and symmetry of cosine
Notice that \(\cos\left(\frac{7\pi}{7}\right) = \cos(\pi) = -1\). So we can rewrite the expression as:
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