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