Solve the equation on the interval $[0,2 \pi)$. \[ 2 \sin 2 x-1=0 \]

Step 1 ：Given the equation \(2 \sin 2x - 1 = 0\).

Step 2 ：Isolate the trigonometric function: \(2 \sin 2x = 1\) which simplifies to \(\sin 2x = 0.5\).

Step 3 ：The solutions to \(\sin 2x = 0.5\) in the interval \([0,2 \pi)\) are approximately 0.2618 and 1.3090.

Step 4 ：Final Answer: The solutions to the equation \(2 \sin 2x - 1 = 0\) in the interval \([0,2 \pi)\) are \(\boxed{0.2618}\) and \(\boxed{1.3090}\).