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 \(x + yz - zx \).