If \(x\), \(y\) and \(z\) are positive real numbers, find the value of the determinant below:

\[\large \begin{vmatrix} 1 & \log_x y & \log_x z \\ \log_y x & 1 & \log_y z \\ \log_z x & \log_z y & 1 \end{vmatrix} \]

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