Determine the possible values of theta: $\sin \theta=\frac{\sqrt{3}}{2}$

Step 1 ：Determine the possible values of theta: $\sin \theta=\frac{\sqrt{3}}{2}$

Step 2 ：The sine function has a value of $\frac{\sqrt{3}}{2}$ at angles of $\frac{\pi}{3}$ and $\frac{2\pi}{3}$ in the unit circle.

Step 3 ：However, since the sine function is periodic with a period of $2\pi$, we can add any integer multiple of $2\pi$ to these angles to get more solutions.

Step 4 ：Therefore, the general solutions to the equation $\sin \theta=\frac{\sqrt{3}}{2}$ are $\theta=\frac{\pi}{3}+2n\pi$ and $\theta=\frac{2\pi}{3}+2n\pi$, where $n$ is an integer.

Step 5 ：Final Answer: The possible values of $\theta$ are $\boxed{\theta=\frac{\pi}{3}+2n\pi}$ and $\boxed{\theta=\frac{2\pi}{3}+2n\pi}$, where $n$ is an integer.