If \({\mathrm{z}}_{1},{\mathrm{z}}_{2},{\mathrm{z}}_{3}\in \mathrm{C}\) are the vertices of an equilateral triangle, who…

If \({\mathrm{z}}_{1},{\mathrm{z}}_{2},{\mathrm{z}}_{3}\in \mathrm{C}\) are the vertices of an equilateral triangle, whose centroid is \({z}_{0}\), then \(\sum _{k=1}^{3}{\left({z}_{k}-{z}_{0}\right)}^{2}\) is equal to

[JEE Main 2025, 3 Apr (Shift 2)]