Let Z_1,Z_2,Z_3 be 3 non-zero complex numbers and Z_1\neq Z_2 if \left|\begin{array}{ccc}|Z_1|&|Z_2|&|Z_3|\\|Z_2|&|  Z_3|&|Z_1|\\|Z_3|&|Z_1|&|Z_2|\end{array}\right| = 0,
then prove that:

\arg \left(\frac{Z_3}{Z_2}\right) = \arg \left(\frac{Z_3 - Z_1}{Z_2 - Z_1}\right)^2