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

What are the solutions to $\sec \frac{3 \theta}{2}=-2$ in the interval $0 \leq \theta< 2 \pi$ ? 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 \( 0 \leq x<2 \pi \). 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 \( 0 \leq \theta<2 \pi \).

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

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