Answer
$\frac{\pi}{2}$
Work Step by Step
1. $2sin^2\theta-5sin\theta+3=0 \Longrightarrow (2sin\theta-3)(sin\theta-1)=0 \Longrightarrow sin\theta=\frac{3}{2}, sin\theta=1$,
2. $sin\theta=\frac{3}{2} \Longrightarrow $ no solution in $[0,2\pi)$,
3. $sin\theta=1 \Longrightarrow \theta=\frac{\pi}{2}$ in $[0,2\pi)$.
