Sequential Stern-Gerlach Experiments 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.
 A: Not surprisingly, such questions date back to the original Stern-Gerlach experiments.  An early experiment, perhaps not exactly what you seek, is reported by TE Phipps and O Stern (yes, the same Stern) in Zeitschrift fur Physik 73(3-4) 185-191 (1932). Another, more recent article, is K. Brodsky et al., Europhysics Letters 44(2) 137-143 (1998) on 'Single and double interaction zone with comoving fields in Stern-Gerlach atom interferometry' - this is probably way more sophisticated that you seek, but shows that double Stern-Gerlach experiments are not uncommon, but perhaps not called that.  
A nice article that covers most of the related theory in an accessible way is AR Mackintosh, 'The Stern-Gerlach experiment, electron spin and intermediate quantum mechanics', Eur. J. Phys 4 97-106 (1983).  This is theory only. 
A: I don't know if precisely this experiment has been done, but experiments close to it have been done in various interference experiments with atoms and neutrons. However, I would like to suggest that the question comes from a misunderstanding of how physics makes progress. It is neither necessary nor useful to demonstrate directly every application of some concept in physics. Rather, we use the fact that the subject is a logical construct that hangs together, and we build up experimental support for the whole structure. In the case of quantum theory and spin angular momentum, there is a huge wealth of experimental support for the theory, whether or not anyone ever does precisely an experiment with a sequence of two Stern-Gerlach-style apparatuses using magnetic field gradients to redirect particles according to their spin state.
