Given:
$$\frac{d\theta}{dt}=2$$
$$y = r(\sin\theta)=(3 \theta+\sin \theta)(\sin \theta)$$
Find $\dfrac{dy}{dt} = \dfrac{\left(\dfrac{dy}{d \theta}\right)}{\left( \dfrac{dt}{d \theta}\right)} = \dfrac{dy}{d \theta}\cdot \dfrac{d \theta}{dt} = \text{ ??}$
Yes, where $\theta = \frac{2 \pi}{3}$ and am supposed to get an answer of -2.819
I agree with value $-2.819...$ because the derivative of
$$\rho = r(\sin\theta)=(3 \theta+\sin \theta)(\sin \theta)$$
with respect to $\theta$ is
$$(3 +\cos\theta)(\sin \theta)+(3 \theta+\sin \theta)(\cos \theta)$$
whose value for $\theta=2 \pi/3$ is $\sqrt{3}-\pi=-1.40954$.
Then, you just have to multiply by the other derivative, i.e., multiply by 2...
Remark: notation $y$ is very misleading as some colleagues remarked it. It should be replaced (as I have done) by $r$ or $\rho$.