if cosA+cosB+cosC=0=sinA+sinB+sinC

prove that

cos^2 A + cos^2 B + cos^2 C = sin^2 A + sin^2 B + sin^2 C = 3/2

I have no idea how to equate the two. This was part of the questions in the chapter on complex numbers, so perhaps I should have included it in number theory. Butanyproof is welcome.