I know this isn’t how StackExchange works, but I needed to comment on the answer to this question and I don’t have enough reputation to do so (or enough time to gain enough).
I intended to ask why it is sufficient to show only that the $\phi$ component is equal to $0$. I understand how to show that $r^2\dot\phi\sin^2\theta$ being constant means that the $\phi$ component is $0$, but I couldn’t work out how to show that this also means the $\theta$ component is equal to $0$, despite the answer to the linked question implying that the $\theta$ component doesn’t necessarily have to equal $0$.
Also, I’m aware that this question probably counts as a duplicate, but I couldn’t see another way of asking without somehow gaining 42 reputation in less than two hours.
It's given in the problem that the acceleration is radial only, so we know acceleration in the $\phi$ and $\theta$ components are both $0$. As it turns out, to solve the problem, all we need is that acceleration in the $\phi$ component is $0$; the fact that acceleration in the $\theta$ component is $0$ is extraneous information.