  We analyze the neutrino conversions inside a supernova in the 3$\nu$ mixing
scheme, and their effects on the neutrino spectra observed at the earth. We
find that the observations of the energy spectra of neutrinos from a future
galactic supernova may enable us to identify the solar neutrino solution, to
determine the sign of $\Delta m^2_{32}$, and to probe the mixing matrix element
|U_{e3}|^2 to values as low as 10^{-4}-10^{-3}.
