If $Z_1$ , $Z_2$ and $Z_3$ are complex numbers such that $|Z_1| + |Z_2| + |Z_3| = |Z_1 + Z_2 + Z_3|$ then find the value of , $\frac{Z_1Z_2}{{Z_3}^2} + \frac{Z_2Z_3}{{Z_1}^2} + \frac{Z_1Z_3}{{Z_2}^2}$
Accordingly to the solution of the above problem , the data given the problem suggests that $0$ , ${Z_1}$ , ${Z_2}$ , ${Z_3}$ are collinear . How can we derive that from the data given in the problem ? And even if we do , how do we know for certain that the points are collinear with the origin on the real axis and not in the imaginary axis ? Then how can we proceed with the solution ? Please help.