Answer
$\frac{\pi}{6}, \frac{5\pi}{6},\frac{7\pi}{6}, \frac{11\pi}{6}$.
Work Step by Step
Step 1. Solve the equation $4sin^2x=1$ to get $sin(x)=\pm\frac{1}{2}$
Step 2. For $sin(x)=\frac{1}{2}$, we have solutions in $[0,2\pi)$ as $x=\frac{\pi}{6}, \frac{5\pi}{6}$
Step 3. For $sin(x)=-\frac{1}{2}$, we have solutions in $[0,2\pi)$ as $x=\frac{7\pi}{6}, \frac{11\pi}{6}$
Step 4. Thus, we have all the solutions in $[0,2\pi)$ as $x=\frac{\pi}{6}, \frac{5\pi}{6},\frac{7\pi}{6}, \frac{11\pi}{6}$.
