Answer
$0.253, 2.889$
Work Step by Step
Step 1. $4sin^2\theta+7sin\theta-2=0 \longrightarrow (4sin\theta-1)(sin\theta+2)=0\longrightarrow sin\theta=\frac{1}{4}$ and $sin\theta=-2$
Step 2. For $sin\theta=\frac{1}{4}$, we have $\theta=2k\pi+sin^{-1}(\frac{1}{4})\approx 2k\pi+0.253$ and $\theta\approx 2k\pi+2.889$
Step 3. Within $[0,2\pi)$, we have $\theta=0.253, 2.889$
