It is known that a right triangle $\triangle A B C$ has side lengths $\overline { A B } = \sqrt { 7 }$, $\overline { A C } = \sqrt { 3 }$, $\overline { B C } = 2$. If isosceles triangles $\triangle M A B$ and $\triangle N A C$ with vertex angles equal to $120 ^ { \circ }$ are constructed outside $\triangle A B C$ using $\overline { A B }$ and $\overline { A C }$ as bases respectively, then $\overline { M N } ^ { 2 } =$ \underline{\hspace{2cm}}. (Express as a fraction in lowest terms)