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We propose a method based on asteroseismology and a Bayesian hierarchical scheme for extracting the inclination angle of a single star. This hierarchical method therefore provides a means to both accurately and robustly extract inclination angles from red giant stars. We successfully apply this technique to an artificial data set with an underlying isotropic inclination angle distribution to verify the method. We also apply this technique to 123 red giant stars observed with Kepler. 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