Consider the complex numbers [tex]z_1, z_2, z_3[/tex] such that [tex](z_3 -z_1)^2 -(z_3 -z_1)(z_2 -z_1)+(z_2 -z_1)^2 =0[/tex]. Given that [tex]z_1, z_2, z_3[/tex] are the vertices of an equilateral triangle, show that [tex]\frac{1}{z_2 -z_1}-\frac{1}{z_1 -z_3}-\frac{1}{z_2 -z_3}=0[/tex].