3. Find all solutions of the equation in the interval $[0,2 \pi)$. \[ (2 \sin x-\sqrt{2})(2 \sin x+\sqrt{3})=0 \]

Step 1 ：The given equation is a product of two terms and it equals zero. This means that at least one of the terms must be zero. Therefore, we can set each term equal to zero and solve for x. The solutions to the equation will be the union of the solutions to these two equations.

Step 2 ：Setting \(2 \sin x - \sqrt{2} = 0\), we find the solutions to be \(x = 0.785398163397448, 2.35619449019234\).

Step 3 ：Setting \(2 \sin x + \sqrt{3} = 0\), we find the solutions to be \(x = -1.0471975511966 + 2\pi, 4.18879020478639\).

Step 4 ：The solutions to the equation are the union of the solutions to the two equations. However, we need to make sure that all solutions are in the interval \([0,2 \pi)\). The solution -1.0471975511966 + 2\pi from the second equation is not in this interval. We need to convert it to the equivalent angle in the interval \([0,2 \pi)\).

Step 5 ：Converting the solution -1.0471975511966 + 2\pi to the equivalent angle in the interval \([0,2 \pi)\), we get \(x = 5.23598775598299\).

Step 6 ：The final solutions to the equation in the interval \([0,2 \pi)\) are \(\boxed{0.785398163397448, 2.35619449019234, 5.23598775598299, 4.18879020478639}\).