Be careful, $a,b,c\ne0$

Algebra Level 3

Let $a$, $b$, and $c$ be non-zero real numbers such that \begin{cases} \begin{aligned} a^2+a&=b^2 \\b^2+b&=c^2 \\c^2+c&=a^2. \end{aligned} \end{cases} Find the value of $(a-b)(b-c)(c-a)$.

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