Complex Equilateral triangle

Geometry Level 4

Let there be an equilateral triangle on the complex plane with vertices \(z_1,z_2,\) and \(z_3\). Let the circumcenter of the triangle be \(z_0\).

If \(z_0\ne 0\), find the value of:

\[ \frac{(z_1)^2+(z_2)^2+(z_3)^2}{(z_0)^2} \]

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