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Thanks for the reply. I'm still a bit lost though, because the cubic equation is x^3 + x^2 - 2x - 1 = 0 (I think). So how do you find the roots to this equation by using x = z + 1/z? I mean there are 7 values for z.

Suppose that z^7 = 1 where z=/=1 (i) Deduce that z^3 + z^2 + z + 1 + 1/z + 1/z^2 + 1/z^3 = 0 (ii) By letting x = z + 1/z reduce the equation in (i) to a cubic equation in x. (iii) Hence deduce that (cos pi/7)(cos 2pi/7)(cos 3pi/7) = 1/8 I got (i) and (ii) but have no idea on how to...