Let $$\left[\cdot\right]$$ be the greatest integer function. If $$(\alpha = \int_{0}^{64} \left( x^{1/3} - [x^{1/3}] \right)\, dx $$, then $$\frac{1}{\pi} \int_{0}^{\alpha\pi } \left( \frac{\sin^{2}\theta } {\sin^{6}\theta + \cos^{6}\theta} \right) d\theta$$ is equal to ____ .