Interactions of three different types of electronic angular momenta, namely, spin, orbital, and total angular momenta from different origins in a photoexcited neutral bis(phthalocyaninato)terbium single-molecule magnet (Pc2Tb, where Pc2- denotes a phthalocyaninato anion) have been studied. We have conducted varied-temperature and varied-magnetic-field magnetic circular dichroism (MCD) measurements on the highest occupied molecular orbital-lowest unoccupied molecular orbital electronic transition in the ligand side of the neutral Pc2Tb to reveal the quantum nature of the system composed of a pi-radical with a spin angular momentum S, the 4f system with a total angular momentum J, and the cyclic pi conjugate system with a photoinduced orbital angular momentum L. We have constructed a new theoretical model that gives a quantitative agreement to the temperature and magnetic field dependence of MCD. The theoretical analysis revealed that the system takes eight quantum states that can be expressed as vertical bar J(z)S(z)L(z)> = I +/-+/-+/->, where the three angular momenta are quantized along the fourfold symmetry axis. Thus, we have identified the existence of the magnetic interactions among the three angular momenta and quantitatively determined their magnitudes for the first time.