Answer
$\left\{0.7297, 2.4116, \frac{\pi}{2}\right\}$
Work Step by Step
Let $u=\sin{x}$
Replacing $\sin{x}$ by $u$ gives:
$3u^2-5u+2=0$
Factor the trinomial to obtain:
$(3u-2)(u-1)=0$
use the Zero Factor Property by equating each factor to zero, then solve each equation to obtain:
\begin{array}{ccc}
&3u-2=0 &\text{or} &u-1=0
\\&3u=2 &\text{or} &u=1
\\&u=\frac{2}{3} &\text{or} &u=1
\end{array}
Substitute $u$ with $\sin{x}$ to obtain:
\begin{array}{ccc}
&\sin{x} = \frac{2}{3} &\text{or} &\sin{x}=1
\\&x=\sin^{-1}{(\frac{2}{3})} &\text{or} &x=\sin^{-1}{(1)}
\\&x=0.7297276562 &\text{or} &x=\frac{\pi}{2}
\end{array}
Note that for an angle $x$ in Quadrant I like $0.7297276562$, the value of $\sin{x}=\sin{(\pi-x)}$.
Thus, $\sin{(0.7297276562)}=\sin{(\pi-0.7297276562)}$.
$\pi-0.7297276562=2.411592654\approx 2.4116$.
Therefore, the solutions to the given equation, rounded-off to four decimal places when necessary, are:
$\left\{0.7297, 2.4116, \frac{\pi}{2}\right\}$
