  We investigate the multi-azimuthal angle (MAA) effect on collective neutrino
oscillation by considering the three-dimensional neutrino momentum distribution
in a realistic electron-capture supernova model with an $8.8 M_{\odot}$
progenitor. We find that the MAA effect induces collective flavor conversions
at epochs when it is completely suppressed under the axial-symmetric
approximation. This novel activity is switched on/off by the growth of the MAA
instability and imprints additional time evolution in the expected neutrino
event rate. We validate our results by extending the linear stability analysis
into the three-flavor scheme including mixing angles, and confirm that the
onset of collective neutrino oscillation matches the steep growth of flavor
instability. We discuss how the MAA effect alters neutrino detection at
Super-Kamiokande and DUNE.
