In order to investigate the impact of collective neutrino oscillations (CNOs) on the neutrino signal from a nearby supernova, we perform three-flavor neutrino oscillation simulations employing the multiangle effect. The background hydrodynamic model is based on the neutrino hydrodynamic simulation of a 8.8 M⊙ progenitor star. We find that CNO commences after some 100 ms post bounce. Before this, CNO is suppressed by matter-induced decoherence. In the inverted mass hierarchy, the spectrum of νe becomes softer after the onset of CNO. To evaluate the detectability of this modification, we define a hardness ratio between the number of high energy neutrino events and low energy neutrino events adopting a fixed critical energy. We show that Hyper-Kamiokande (HK) can distinguish the effect of CNO for supernova distances out to ∼10 kpc. On the other hand, for the normal mass hierarchy, the spectrum of νe becomes softer after the onset of CNO, and we show that DUNE can distinguish this feature for supernova distances out to ∼10 kpc. More work is necessary to optimize the best value of critical energy for maximum sensitivity. We also show that if the spectrum of νe in HK becomes softer due to CNO, the spectrum of νe in DUNE becomes harder, and vice versa. These synergistic observations in νe and νe, by HK and DUNE, respectively, will be an intriguing opportunity to test the occurrence of CNO.