Find the sum of the solutions to
\[2 \sin^3 x - 3 \sin x = -\frac{3}{2} \sin 2x\]in the interval $0 \le x \le 2 \pi.$
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Find the sum of the solutions to
\[2 \sin^3 x - 3 \sin x = -\frac{3}{2} \sin 2x\]in the interval $0 \le x \le 2 \pi.$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
5 \pi
Find the sum of the solutions to
\[2 \sin^3 x - 3 \sin x = -\frac{3}{2} \sin 2x\]in the interval $0 \le x \le 2 \pi.$
train