Answer
The solution of the equation $\sin \theta =\left( \frac{\pi }{6},\frac{5\pi }{6},\frac{\pi }{2} \right)$.
Work Step by Step
When the middle term will be split, the given equation will be:
$\begin{align}
& 2{{\sin }^{2}}\theta -3\sin \theta +1=0 \\
& \left( 2\sin \theta -1 \right)\left( \sin \theta -1 \right)=0
\end{align}$
Therefore, $\sin \theta =\frac{1}{2},1$
The values of $\sin \theta =\frac{1}{2}$ in the interval $\left[ 0,\left. 2\pi \right) \right.$ are $\frac{\pi }{6},\frac{5\pi }{6},\frac{\pi }{2}$.
