Find an angle `theta, 0 lt theta lt pi/2`, which increases twice as fast as its sine.

Explanation

To solve the problem, we need to find an angle \( \theta \) in the interval \( 0 < \theta < \frac{\pi}{2} \) such that the rate of change of \( \theta \) is twice the rate of change of \( \sin(\theta) \).

### Step-by-Step Solution:

1. **Set up the relationship between the rates of change**:
We start with the condition given in the problem:
\[
\frac{d\theta}{dt} = 2 \frac{d(\sin \theta)}{dt}
...