Equal Squares

Algebra Level 5

It is given that aa, bb, and cc are nonzero real numbers such that

(a+b)2=(b+c)2=(c+a)2(a+b)^2 = (b+c)^2 = (c+a)^2

Find the product of all possible distinct values of ab+bc+ca\frac{a}{b} + \frac{b}{c} + \frac{c}{a}.

If you think that the equality has no solution, submit 0 as your answer.

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