Complex Numbers

Let \(Z_1, Z_2\) and \(Z_3\) be three non zero complex numbers such that \(a=\left|Z_1\right|, b=\left|Z_2\right|\) and \(c=\left|Z_3\right|\), if the determinant $$\left|\begin{array}{lll}a & b & c \\ b & c & a \\ c & a & b\end{array}\right|=0$$, then