Answer
$$\frac{1}{2}\left(\sqrt{3}\sin \theta + \cos \theta\right) $$
Work Step by Step
Since
$$\sin(x+y)= \sin x\cos y+\cos x\sin y $$
Then
\begin{align*}
\sin(\theta+30^{\circ})&= \sin \theta\cos 30^{\circ}+\cos \theta\sin 30^{\circ}\\
&= \frac{\sqrt{3}}{2}\sin \theta + \frac{1}{2}\cos \theta\\
&= \frac{1}{2}\left(\sqrt{3}\sin \theta + \cos \theta\right)
\end{align*}