Suppose that a, b, c are non-zero acute angles such that sin(a − b)/ sin(a + b) + sin(b − c)/ sin(b + c) + sin(c − a)/sin(c + a) = 0. Prove that at least two of a, b, c are equal.

I saw this in a math competition and was perplexed by how to solve the problem. If someone could walk me through it step by step, that would be really helpful.