Find the values of theta if 0 <= theta <= pi ? Sin theta = tan theta

To find the values of $\theta$ where $\sin(\theta) = \tan(\theta)$ for $0 \leq \theta \leq \pi$, we can use the trigonometric identities:

1. $\sin(\theta) = \frac{\sin(\theta)}{\cos(\theta)}$ (Definition of tangent)
2. $\sin(\theta) = \frac{\sin(\theta)}{\cos(\theta)}$
3. $\sin(\theta) \cos(\theta) = \sin(\theta)$ (Multiplying both sides by $\cos(\theta)$)
4. $\sin(\theta) \cos(\theta) - \sin(\theta) = 0$
5. $\sin(\theta)(\cos(\theta) - 1) = 0$

This equation is true when either $\sin(\theta) = 0$ or $\cos(\theta) - 1 = 0$.

When $\sin(\theta) = 0$, the solutions are $\theta = 0$ and $\theta = \pi$.

When $\cos(\theta) - 1 = 0$, we have $\cos(\theta) = 1$, which occurs when $\theta = 0$.

Thus, the solutions for $0 \leq \theta \leq \pi$ are $\theta = 0$ and $\theta = \pi$.