An experimental and theoretical analysis of the angular dependence of the diffracted light beams emerging from three-dimensional colloidal photonic crystals is herein presented. Diffracted beams are identified according to their associated reciprocal-lattice vectors, and their intensities are obtained as a function of the zenithal and azimuthal incidence angles. Significant changes in the beam intensities are observed for large zenithal incidence angles as the azimuthal angle is varied. This phenomenon is related to the excitation of new resonant modes inside the photonic crystal which cannot be observed under normal incidence conditions.