It is known that an acoustic wave incident on an infinite array of aligned rectangular blocks of a different acoustic material exhibits total transmission if certain conditions are met [[1]] which relate the unique “intromission” angle of incidence with geometric and material properties of the slab. This extraordinary acoustic transmission phenomenon holds for any slab thickness, making it analogous to a Brewster effect in optics, and is independent of frequency as long as the slab microstructure is sub-wavelength in the length-wise direction. Here we show that the enhanced transmission effect is obtained in a slab with grating elements oriented obliquely to the slab normal. The dependence of the intromission angle   is given explicitly in terms of the orientation angle. Total transmission is achieved at incidence angles  , with a relative phase shift between the transmitted amplitudes of the   and   cases. These effects are shown to follow from explicit formulas for the transmission coefficient. In the case of grating elements that are rigid the results have direct physical interpretation. The analytical findings are illustrated with full wave simulations.