Suppose a beam of particles is prepared with spin in the $+z$ direction (e.g. by a Stern-Gerlach apparatus). Suppose this beam then enters a Stern-Gerlach apparatus with orientation $\theta$ relative to $+z$. Quantum Mechanics predicts that with probability $\cos^2(\theta/2)$ a particle will be deflected in the $+\theta$ direction, and with probability $\sin^2(\theta/2)$ a particle will be deflected in the $-\theta$ direction.
I have not been able to find any published experimental tests of this prediction for arbitrary values of $\theta$. If you know of any, please provide the appropriate citation.
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