Answer
0.85, 2.29
Work Step by Step
$\begin{align}
4\sin\theta-3&=0\\
4\sin\theta&=3\\
\sin\theta&=\frac{3}{4}
\end{align}$
Since $\sin \theta$ is positive in the first and second quadrants, the only values of $\theta$ in the interval $[0, 2\pi)$ that satisfy the equation are $\sin^{-1}(\frac{3}{4})\approx 0.85$ and $\pi-\sin^{-1}(\frac{3}{4})\approx 2.29$.
