Let [·] be the greatest integer function. If α=∫_0^64(x^1 / 3-[x^1 / 3]) d x, then 1/(π) ∫_0^α π((sin^2 θ)/(sin^6 θ+ cos^6 θ)) d θ is equal to ____.

Let $\displaystyle [\cdot]$ be the greatest integer function. If $\displaystyle \alpha=\int_0^{64}\left(x^{1 / 3}-\left[x^{1 / 3}\right]\right) \mathrm{d} x$, then $\displaystyle \frac{1}{\pi} \int_0^{\alpha \pi}\left(\frac{\sin ^2 \theta}{\sin ^6 \theta+\cos ^6 \theta}\right) \mathrm{d} \theta$ is equal to $\displaystyle \_\_\_\_$.