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Using the factorisation of z⁷ - 1 into linear and quadratic factors over the reals, the value of the product cos(pi/7)*cos(2*pi/7)*cos(3*pi/7) is:

1. 1/8
2. 1/4
3. -1/8
4. 1/2

Correct answer: 1/8

Solution

Factoring z⁷ - 1 and evaluating the cosine product via the roots of unity gives cos(pi/7)*cos(2*pi/7)*cos(3*pi/7) = 1/8.

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