Marinada '26

[lang=hr] Neka su $z_1, z_2, z_3, ..., z_{2025}$ različitih $2025$ rješenja kompleksne jednadžbe $z^{2026}=1$ bez rješenja $z=1$. Odredi vrijednost sume $$S=\sum_{k=1}^{2025} \frac{1}{z_k^2-z_k+1}$$ [/lang] [lang=en] Let $z_1, z_2, z_3, ..., z_{2025}$ be $2025$ different solutions of complex equation $z^{2026}=1$ excluding the solution $z=1$. Find the value of the sum $$S=\sum_{k=1}^{2025} \frac{1}{z_k^2-z_k+1}$$ [/lang]