The real numbers \(a,b,c\) are non-zero and satisfy the following equations: \[\left\{ \begin{array}{l} a^2 +a = b^2 \\ b^2 +b = c^2 \\ c^2 +c = a^2. \end{array} \right.\] Show that \((a-b)(b-c)(c-a)=1\).