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If $a+b+c = 0$ and $abc \neq 0$, then find the value of $\frac { { a }^{ 4 } + { b }^{ 4 } + { c }^{ 4 } } { { a }^{ 2 }{ b }^{ 2 }+ { b }^{ 2 }{ c }^{ 2 }+ { c }^{ 2 }{ a }^{ 2 } }$.

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