1. **Problem statement:** Solve the trigonometric equation $$\sin \theta = 2\theta$$ graphically for $$-\frac{\pi}{2} < \theta < \frac{\pi}{2}$$. 2. **Formula and rules:** The sine function $$\sin \theta$$ ranges between -1 and 1 for all real $$\theta$$. The right side $$2\theta$$ is a linear function. 3. **Graphical approach:** To solve $$\sin \theta = 2\theta$$ graphically, plot both $$y = \sin \theta$$ and $$y = 2\theta$$ on the same axes and find their intersection points within the interval $$-\frac{\pi}{2} < \theta < \frac{\pi}{2}$$. 4. **Analysis:** Since $$2\theta$$ is linear and $$\sin \theta$$ is bounded between -1 and 1, the intersection points must satisfy $$-1 \leq 2\theta \leq 1$$, which implies $$-\frac{1}{2} \leq \theta \leq \frac{1}{2}$$. 5. **Intermediate work:** Check endpoints and behavior: - At $$\theta = 0$$, $$\sin 0 = 0$$ and $$2 \times 0 = 0$$, so $$\theta = 0$$ is a solution. - For $$\theta > 0$$, $$2\theta$$ grows faster than $$\sin \theta$$, so no other intersections. - For $$\theta < 0$$, similarly, no other intersections. 6. **Conclusion:** The only solution in $$-\frac{\pi}{2} < \theta < \frac{\pi}{2}$$ is $$\theta = 0$$. Final answer: $$\boxed{0}$$