The [3]He(α, γ)[7]Be reaction takes place in two distinct astrophysical scenarios. First, in solar hydrogen burning, [3]He(α, γ)[7]Be controls the competition between the pp-I chain, on the one hand, and the pp-II and -III chains, on the other hand. Its rate directly affects the solar model predictions for the well-measured [7]Be and [8]B solar neutrino fluxes, which can in principle be used as solar thermometer. Second, in Big Bang nucleosynthesis, [3]He(α, γ)[7]Be is the main production channel for primordial [7]Li, the decay product of [7]Be. The cross section of this reaction has been studied previously using different methods, namely [7]Be activation, [7]Be recoil detection, and in-beam γ-ray detection. The latter studies have in many cases been performed with just one detector in close geometry. Here, for the first time a comprehensive measurement of the [3]He(α, γ)[7]Be γ-ray angular distribution is reported. Altogether 22 high-purity germanium detectors were used, arranged at 27-145° angle with respect to the beam direction. Data were taken at 442-1213 keV center-of-mass energy. In addition, one data point for the astrophysical S-factor was obtained with the activation method. The angular data are compared with the predictions from a hybrid theoretical approach, where the E1 transitions are modeled using a cluster-based effective field theory (EFT) while the M1 and E2 transitions within an EFT-inspired framework. Good agreement is found, if the interference among these multipolarities is taken into account in the theory.