Solution
= Solution
On the equatorial plane, the only potentially relevant angular connection coefficient is $\Gamma^\theta_{\phi\phi}=-\sin\theta\cos\theta$, which vanishes at $\theta=\pi/2$. The $\theta$ transport equation is consequently $ds^\theta/dt=0$. Since the initially radial spin has $s^\theta(0)=0$,
$$
\boxed{s^\theta(t)=0}.
$$