Answer
$$\frac{\pi}{6}$$
Work Step by Step
\begin{align*}
\lim _{x\rightarrow \frac{\pi}{6}} \frac{ x}{\sin 3x}&= \frac{ \pi/6}{\sin 3\pi/6} \\
&= \frac{ \pi/6}{\sin (3\pi/6)} \\
&= \frac{ \pi/6}{\sin (\pi/2)}\\
&= \frac{\pi}{6}.
\end{align*}
Where we used Theorem 2 -- that is, $\lim _{x\rightarrow 0}\frac{ \sin x}{ x}=1. $
