Solve the equation for exact solutions over the interval $[0,{360}^{\circ })$.
$$\sin (3\theta )=-1$$
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The solution set is
(Simplify your answer. Type your answer in degrees. Do not include the degree symbol in your answer. Use a comma to separate answers as needed.)
B. The solution is the empty set.

Step 1 ：The equation $\sin (3\theta )=-1$ implies that $3\theta$ is an angle whose sine is -1.

Step 2 ：The sine function has a value of -1 at ${270}^{\circ }$ in the unit circle.

Step 3 ：However, since the sine function has a period of ${360}^{\circ }$, we can add any multiple of ${360}^{\circ }$ to ${270}^{\circ }$ and the sine of the resulting angle will still be -1.

Step 4 ：Therefore, the general solution to the equation is $3\theta ={270}^{\circ }+{360}^{\circ }n$, where $n$ is an integer.

Step 5 ：Solving for $\theta$ gives $\theta ={90}^{\circ }+{120}^{\circ }n$.

Step 6 ：We are asked to find the solutions in the interval $[0,{360}^{\circ })$. So, we need to find the integer values of $n$ that make $\theta$ fall in this interval.

Step 7 ：The solutions are ${90}^{\circ }$, ${210}^{\circ }$, and ${330}^{\circ }$.

Step 8 ：Final Answer: The solution set is $\boxed{{\displaystyle {90}^{\circ },{210}^{\circ },{330}^{\circ }}}$.