Answer
$\frac{3\pi}{2}$
Work Step by Step
Step 1. Rewrite the equation $4+4sin\theta=1-sin^2\theta \longrightarrow sin^2\theta+4sin\theta+3=0 \longrightarrow (sin\theta+1)(sin\theta+3)=0$. Thus $sin\theta=-1$ or $sin\theta=-3$.
Step 2. For $sin\theta=-1$, we have $\theta=\frac{3\pi}{2}$
Step 3. For $sin\theta=-3$, we have $\theta=none$
