Let ${{z}_{1}},{{z}_{2}}$ and ${{z}_{3}}$ be three complex numbers on the circle $|z|=1$ with $\arg \left( {{{z}_{1}}} \right)=\frac{{-\pi }}{4},\arg \left( {{{z}_{2}}} \right)=0$ and $\arg \left( {{{z}_{3}}} \right)=\frac{\pi }{4}$. If ${{\left| {{{z}_{1}}{{{\bar{z}}}_{2}}+{{z}_{2}}{{{\bar{z}}}_{3}}+{{z}_{3}}{{{\bar{z}}}_{1}}} \right|}^{2}}=\alpha +\beta \sqrt{2},\alpha ,\beta \in \mathbf{Z}$, then the value of ${{\alpha }^{2}}+{{\beta }^{2}}$ is: