Evaluate: `int_0^(pi//2)sqrt(costheta)sin^3theta`d`theta`

Explanation

To evaluate the integral \( I = \int_0^{\frac{\pi}{2}} \sqrt{\cos \theta} \sin^3 \theta \, d\theta \), we can follow these steps:

### Step 1: Rewrite the integral
We can express \( \sin^3 \theta \) in terms of \( \sin^2 \theta \):
\[ I = \int_0^{\frac{\pi}{2}} \sqrt{\cos \theta} \sin^2 \theta \sin \theta \, d\theta \]
Using the identity \( \sin^2 \theta = 1 - \cos^2 \theta \), we rewrite the integral:
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