Answer
$\color{blue}{270^o}$
Work Step by Step
Let $u=\sin{\theta}$
Replacing $\sin{\theta}$ with $u$ gives:
$u^2+3u+2=0$
Factor the trinomial to obtain:
$(u+2)(u+1)=0$
Use the Zero Factor Property by equating each factor to zero, then solve each equation to obtain:
\begin{array}{ccc}
&u+2=0 &\text{or} &u+1=0
\\&u=-2 &\text{or} &u=-1
\end{array}
Replace $u$ with $\sin{\theta}$ to obtain:
\begin{array}{ccc}
&\sin{\theta}=-2 &\text{or} &\sin{\theta}=-1
\\&(\text{no solution}) &\text{or} &\theta=-90^o
\end{array}
Since the period of $\sin{\theta}$ is $360^o$, then the following is also a solution of the given equation:
$-90^o+360^o=270^o$
Note that $-90^o$ is not within the interval $[0,^o, 360^o)$.
Therefore, the solution to the given equation is $\color{blue}{270^o}$.
