The optical properties of particularly the tungsten-based transition-metal dichalcogenides are strongly influenced by the presence of dark excitons. Recently, theoretical predictions as well as indirect experimental insights have shown that two different dark excitons exist within the light cone. While one is completely dark, the other one is only dipole forbidden out-of-plane, hence referred to as grey exciton. Here, we present angle-resolved spectroscopic data of a high-quality hexagonal-BN-encapsulated WSe2 monolayer with which we directly obtain the radiation pattern of this grey exciton that deviates from that of the bright exciton and other exciton complexes obtained at cryogenic temperatures.