  We develop a framework for studying collective three-flavor neutrino
oscillations based on the density matrix formalism. We show how techniques
proven useful for collective two-flavor neutrino oscillations such as
corotating frames can be applied readily to three-flavor mixing. Applying two
simple assumptions and the conservation of two ``lepton numbers'' we use this
framework to demonstrate how the adiabatic/precession solution emerges. We
illustrate with a numerical example how two stepwise spectral swaps appear
naturally if the flavor evolution of the neutrino gas can be described by such
a solution. For the special case where mu and tau flavor neutrinos are equally
mixed and are produced with identical energy spectra and total numbers, we find
that one of the spectral swaps in the three-flavor scenario agrees with that in
the two-flavor scenario when appropriate mixing parameters are used. Using the
corotating frame technique we show how the adiabatic/precession solution can
obtain even in the presence of a dominant ordinary matter background. With this
solution we can explain why neutrino spectral swapping can be sensitive to
deviations from maximal 23-mixing when the ``mu-tau'' matter term is
significant.
