Find all solutions of the equation given below for $0 \leq t \leq \frac{4 \pi}{3}$. Give exact answers in radians. \[ -2 \sin 3 t=1 \]

Step 1 ：Given the equation \(-2 \sin 3 t=1\), we first isolate the trigonometric function to get \(\sin 3t = -0.5\).

Step 2 ：We then use the inverse sine function to find the value of \(3t\).

Step 3 ：Since the range of \(t\) is given as \(0 \leq t \leq \frac{4 \pi}{3}\), we need to find all possible values of \(t\) within this range.

Step 4 ：By solving, we find the values of \(t\) to be approximately 1.2217304763960308, 0.8726646259971647, and 2.2689280275926285.

Step 5 ：Converting these decimal values to radians, we get \(t = \frac{7\pi}{12}\), \(t = \frac{5\pi}{12}\), and \(t = \frac{11\pi}{6}\).

Step 6 ：\(\boxed{\text{Final Answer: The solutions of the equation } -2 \sin 3 t=1 \text{ for } 0 \leq t \leq \frac{4 \pi}{3} \text{ are } t = \frac{7\pi}{12}, t = \frac{5\pi}{12}, \text{ and } t = \frac{11\pi}{6}.}\)