Solve the equation on the interval $0\le \theta <2\pi$.
$$\sec \frac{3\theta }{2}=-2$$

What are the solutions to $\sec \frac{3\theta }{2}=-2$ in the interval $0\le \theta <2\pi$ ? Select the correct choice and fill in any answer boxes in your choice below.
A. The solution set is
(Simplify your answer. Type an exact answer, using $\pi$ as needed. Type your answer in radians. Use integers or fractions for any numbers in the expression. Use
B. There is no solution.

Step 1 ：The secant function is the reciprocal of the cosine function. So, we can rewrite the equation as $\cos \frac{3\theta }{2}=-\frac{1}{2}$.

Step 2 ：The cosine function equals -1/2 at $\frac{2\pi }{3}$ and $\frac{4\pi }{3}$ in the interval $0\le x<2\pi$. However, we need to find the solutions for $\frac{3\theta }{2}$, not $x$. So, we need to solve the equation $\frac{3\theta }{2}=\frac{2\pi }{3}$ and $\frac{3\theta }{2}=\frac{4\pi }{3}$ for $\theta$.

Step 3 ：The solutions to the equations are $\theta =\frac{4\pi }{9}$ and $\theta =\frac{8\pi }{9}$. However, we need to check if these solutions are in the interval $0\le \theta <2\pi$.

Step 4 ：Both solutions are in the interval $0\le \theta <2\pi$. Therefore, the solutions to the equation $\sec \frac{3\theta }{2}=-2$ in the interval $0\le \theta <2\pi$ are $\theta =\frac{4\pi }{9}$ and $\theta =\frac{8\pi }{9}$.

Step 5 ：Final Answer: The solution set is $\boxed{{\displaystyle \frac{4\pi }{9},\frac{8\pi }{9}}}$.