If cos(a-b) + cos(b-c) + cos(c-a) = 3/2,
the prove that cos(a) + cos(b) + cos(c) = sin(a) + sin(b) + sin(c) = 0.
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did you even try?
expand out the first line using $\cos(x-y)=\cos(x)\cos(y)+\sin(x)\sin(y)$ and see where that leads.
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