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In physics, the Brewster effect initially refers to a reflectionless transmission of a transverse-magnetic wave that impinges on an interface separating two different regular media at a particular angle, known as the Brewster angle. Nowadays, people have recognized that the Brewster effect can also be observed under transverse-electric incidences such as in magnetic media. However, all Brewster effects observed so far were associated with a unique incident angle. In this work, we demonstrate a Terahertz metasurface on which the Brewster effect can be observed at all angles of incidence. The underlying physics behind this all-angle Brewster effect is the dispersion engineered at each angle of incidence to strictly match the longitudinal wave impedance on both sides of the surface. Theoretical analysis, full-wave simulation, and experimental results are consistent with each other. The proposed approach is simple but robust and scalable to other frequencies, implying promising applications such as perfect polarizers and space phase shifters.