A complex number z is said to be unimodular if $\,\left| z \right| = 1$. Suppose ${z_1}$ and ${z_2}$ are complex numbers such that ${{{z_1} - 2{z_2}} \over {2 - {z_1}\overline {{z_2}} }}$ is unimodular and ${z_2}$ is not unimodular. Then the point ${z_1}$ lies on a :