Answer
$$
\frac{d y}{d x}= -\frac{1}{3\sin \theta \cos \theta}
$$
and at $\theta=\pi/4$, we have
$$
\frac{d y}{d x}=-\frac{2}{3}.
$$
Work Step by Step
Since $x=\sin^3\theta $ and $y=\cos \theta$, then we have
$$
\frac{d y}{d x}= \frac{y^{\prime}}{x^{\prime}}=\frac{- \sin\theta}{3\sin^2 \theta \cos \theta}=-\frac{1}{3\sin \theta \cos \theta}
$$
and at $\theta=\pi/4$, we have
$$
\frac{d y}{d x}=- \frac{1}{3(1/2)}=-\frac{2}{3}.
$$
