  In this paper, we first calculate the realistic Earth matter effects in the
detection of type II supernova neutrinos at the Daya Bay reactor neutrino
experiment which is currently under construction. It is found that the Earth
matter effects depend on the neutrino incident angle $\theta$, the neutrino
mass hierarchy $\Delta m_{31}^{2}$, the crossing probability at the high
resonance region inside the supernova, $P_{H}$, the neutrino temperature,
$T_{\alpha}$, and the pinching parameter in the neutrino spectrum,
$\eta_{\alpha}$. We also take into account the collective effects due to
neutrino-neutrino interactions inside the supernova. With the expression for
the dependence of $P_H$ on the neutrino mixing angle $\theta_{13}$, we obtain
the relations between $\theta_{13}$ and the event numbers for various reaction
channels of supernova neutrinos. Using these relations, we propose a possible
method to acquire information about $\theta_{13}$ smaller than $1.5^\circ$.
Such a sensitivity cannot yet be achieved by the Daya Bay reactor neutrino
experiment which has a sensitivity of the order of $\theta_{13}\sim 3^\circ$.
Furthermore, we apply this method to other neutrino experiments, i.e. Super-K,
SNO, KamLAND, LVD, MinBooNE, Borexino, and Double-Chooz. We also study the
energy spectra of the differential event numbers, ${\rm d}N/{\rm d}E$.
