 Spin measurement in the yz plane

For a state initially $z$-up and precessing about $y$, measurement along $\mathbf{n}=(0,\sin \theta ,\cos \theta )$ has the displayed probabilities. eigenvectors can be chosen as $(\cos (\theta /2),i\sin (\theta /2){)}^T$ and $(i\sin (\theta /2),\cos (\theta /2){)}^T$. Their phases must be retained when taking inner products. Full $2\pi$ rotation changes their signs but leaves isolated-state probabilities unchanged.