Answer
$$x=0.15 ,\:x=\frac{\pi -0.305}{2},\:x=3.293 ,\:x=4.56 $$
Work Step by Step
Solving the equation using inverse trigonometric functions, we find:
$$\sin \left(2x\right)=0.3,\:0\le \:x\le \:2\pi \\ x=\frac{\arcsin \left(0.3\right)+2\pi n}{2},\:x=\frac{\pi -\arcsin \left(0.3\right)+2\pi n}{2} \\ x=0.15 ,\:x=\frac{\pi -0.305}{2},\:x=3.293 ,\:x=4.56 $$