Answer
$0.253,2.889$
Work Step by Step
1. $4sin^2(\theta)+7sin\theta-2=0\Longrightarrow (4sin\theta-1)(sin\theta+2)=0\Longrightarrow sin(\theta)=-2$ (no solution) or $sin(\theta)=\frac{1}{4}$
2. For $sin(\theta)=\frac{1}{4}$, we have $\theta\approx 2k\pi+0.253$ or $\theta\approx 2k\pi+2.889$
3. Within $[0,2\pi)$, we have $\theta=0.253,2.889$
