Estimate $\left(\frac{\cos\left(\frac{\pi}{2}\cdot\cos\theta\right)}{\sin\theta}\right)^2$

Question

I need to show that: $\left(\frac{\cos\left(\frac{\pi}{2}\cdot\cos\theta\right)}{\sin\theta}\right)^2\simeq \sin^3(\theta)$

I used Matlab, their graphs are very similar. How to prove above estimate?