$\displaystyle \lim_{x\to\frac{\pi}{2}} \left( \frac{1}{(x-\frac{\pi}{2})^{2}}\, \frac{\left(\frac{\pi}{3}\right)^{3}}{x^{3}} \int_{0}^{x}\cos\!\left(t^{1/3}\right)\,dt \right)$ is equal to: