Let \( \int x^3 \sin x \, dx = g(x) + C \), where \( C \) is the constant of integration. If \( 8 \left( g\left(\frac{\pi}{2}\right) + g'\left(\frac{\pi}{2}\right)\right) = \alpha \pi^3 + \beta \pi^2 + \gamma, \alpha, \beta, \gamma \in \mathbb{Z} \), then \( \alpha + \beta - \gamma \) equals