Answer
$$
\frac{d y}{d x}= \frac{-3\sin3\theta}{2\cos 2\theta}
$$
and at $\theta=\pi/6$, we have
$$
\frac{d y}{d x}=-3.
$$
Work Step by Step
Since $x=\sin 2\theta $ and $y=\cos 3\theta$ then we have
$$
\frac{d y}{d x}= \frac{y^{\prime}}{x^{\prime}}=\frac{-3\sin3\theta}{2\cos 2\theta}
$$
and at $\theta=\pi/6$, we have
$$
\frac{d y}{d x}=- \frac{3}{2(1/2)}=-3.
$$
