Really finding roots

Algebra Level 5

\[ \begin{eqnarray} a+b+c &=& abc \\ ab +bc + ca &=& 1 \\ a^2+b^2 + c^2 &=& 1 \\ \end{eqnarray} \]

Let \(a,b,c\) be complex numbers satisfying the system of equations above. What is the value of \(|a|^2+|b|^2+|c|^2 \)?

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