Mathematics - Complex Number Question with Solution | TestHub

For a non-zero complex number $z$, let $\arg (z)$ denote the principal argument of $z$, with $-\pi <\arg (z)\le \pi$. Let $\omega$ be the cube root of unity for which $0<\arg (\omega )<\pi$. Let $\alpha =\arg \left({\sum }_{n=1}^{2025}(-\omega {)}^n\right)$. Then the value of $\frac{3\alpha }{\pi }$ is ___________