Find all values of $\theta$ if $\theta$ is in the interval $[0^{\circ },{360}^{\circ })$ and has the given function value.
$$\sin \theta \approx 0.4999161$$
The value(s) of $\theta$ is/are
(Round to five decimal places as needed. Use a comma to separate answers as needed. Do not include the degree symbol in your answer.)

Step 1 ：Given that $\sin \theta \approx 0.4999161$, we need to find all values of $\theta$ in the interval $[0^{\circ },{360}^{\circ })$.

Step 2 ：The sine function has a period of ${360}^{\circ }$, and it is positive in the first and second quadrants.

Step 3 ：First, we find the value of $\theta$ in the first quadrant by taking the inverse sine of the given value. This gives us $\theta \approx {29.99445}^{\circ }$.

Step 4 ：Next, we use the symmetry of the sine function to find the value in the second quadrant. Since the sine function is symmetric about ${90}^{\circ }$, the value of $\theta$ in the second quadrant is ${180}^{\circ }-{29.99445}^{\circ }\approx {150.00555}^{\circ }$.

Step 5 ：Final Answer: The values of $\theta$ are approximately $\boxed{{\displaystyle {29.99445}^{\circ }}}$ and $\boxed{{\displaystyle {150.00555}^{\circ }}}$.