Complex Equilateral triangle

Geometry Level 3

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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