ComplexNumberBasic Intermediate

Problem - 2188
If complex numbers $z_1, z_2, z_3$ satisfy $$ \left\{ \begin{array}{l} |z_1|=|z_2|=|z_3|=1\\ \\ \displaystyle\frac{z_1}{z_2}+\frac{z_2}{z_3}+\frac{z_3}{z_1}=1 \end{array} \right. $$ Compute $|az_1 +bz_2+cz_3|$ where $a, b, c$ are three given real numbers.

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