Equal in proportion

Algebra Level 4

$\begin{eqnarray} 2x-2y + \frac 1 z &=& \frac 1 {2014} \\ 2y - 2z + \frac 1 x &=& \frac 1 {2014} \\ 2z - 2x + \frac 1 y &=& \frac 1 {2014} \\ \end{eqnarray}$

Find all positive real numbers $$x,y,z$$ such that they satisfy the system of equation above. Submit your answer as $$x + yz - zx$$.

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