Answer
There are only 1 value of $x$ satisfying the equation, which is $$x=\frac{\pi}{2}$$
Work Step by Step
$$\sin x+2=3$$ $$\sin x=1$$
In the interval $[0,2\pi)$, there are only 1 value of $x$ satisfying the equation, which is $$x=\frac{\pi}{2}$$
*NOTES: For $\sin x=a$, except when $\sin x=0$, the set of values of satisfying $x$ is $x=u+2\pi$, which means for $\sin x$ to reach a specific amount again, the cycle has to go through $2\pi$, or in fact a full circle.
