Prime Again?

\[\large{\begin{cases} x^2 + xy + y^2 &=& 19 \\ y^2 + yz + z^2 &=& 67 \\ z^2 + zx + x^2 &=& 79 \\ \end{cases} } \]

Considering the system of Diophantine equations above, what is the value of \(xy + yz +zx\) ?

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