The quantum theory of a singlet spin-\textonehalf{} system is developed in terms of angular variables using a quantum-distribution-function technique. These calculations demonstrate a much closer correspondence between quantum mechanics and certain hidden-variable theories than was previously appreciated. It is found that a new type of hidden-variable theory is suggested by the quantum-distribution-function treatment of the Einstein-Podolsky-Rosen-Bohm spin-spin correlation problem which is in agreement with quantum theory but is "nonlocal."