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The basic features of obliquely propagating dust-acoustic solitary waves (DASWs), and their multidimensional instability in a magnetized dusty plasma containing negatively charged dust, two-temperature electrons, and trapped ions, have been theoretically investigated by the reductive-perturbation method and small-k perturbation-expansion technique. The combined effects of external magnetic field (obliqueness), two-electron temperature, and trapped-ion distribution, which are found to significantly modify the basic properties (amplitude and width) of small but finite-amplitude DASWs, are explicitly examined. It is also found that the instability criterion and the growth rate are significantly modified by the external magnetic field and the propagation directions of both the nonlinear waves and their perturbation modes. The implications of our results in space plasmas are briefly discussed.