1. The problem asks to find the angle $\theta$ in radians such that $\sin \theta = \frac{\sqrt{2}}{2}$. 2. Recall that on the unit circle, the sine of an angle $\theta$ corresponds to the $y$-coordinate of the point on the circle at that angle. 3. The value $\frac{\sqrt{2}}{2}$ is a well-known sine value corresponding to angles of $45^\circ$ and $135^\circ$ in degrees. 4. To convert degrees to radians, use the formula: $$\text{radians} = \text{degrees} \times \frac{\pi}{180}$$ 5. Calculate the radians for $45^\circ$: $$45^\circ \times \frac{\pi}{180} = \frac{\pi}{4}$$ 6. Calculate the radians for $135^\circ$: $$135^\circ \times \frac{\pi}{180} = \frac{3\pi}{4}$$ 7. Therefore, the angles $\theta$ in radians where $\sin \theta = \frac{\sqrt{2}}{2}$ are: $$\theta = \frac{\pi}{4} \text{ and } \theta = \frac{3\pi}{4}$$ 8. These correspond to the points $\left(\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}\right)$ and $\left(-\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}\right)$ on the unit circle. Final answer: $$\boxed{\theta = \frac{\pi}{4} \text{ or } \frac{3\pi}{4}}$$