Be careful, \(a,b,c\ne0\)

Algebra Level 3

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

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