Complex Equilateral triangle

Geometry Level 2

Let there be an equilateral triangle on the complex plane with vertices z1,z2,z_1,z_2, and z3z_3. Let the circumcenter of the triangle be z0z_0.

If z00z_0\ne 0, find the value of

(z1)2+(z2)2+(z3)2(z0)2. \frac{(z_1)^2+(z_2)^2+(z_3)^2}{(z_0)^2}.

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