  We identify three independent two-fold parameter degeneracies (\delta,
\theta_{13}), sgn(\delta m^2_{31}) and (\theta_{23}, \pi/2-\theta_{23})
inherent in the usual three-neutrino analysis of long-baseline neutrino
experiments, which can lead to as much as an eight-fold degeneracy in the
determination of the oscillation parameters. We discuss the implications these
degeneracies have for detecting CP violation and present criteria for breaking
them. A superbeam facility with a baseline at least as long as the distance
between Fermilab and Homestake (1290 km) and a narrow band beam with energy
tuned so that the measurements are performed at the first oscillation peak can
resolve all the ambiguities other than the (\theta_{23}, \pi/2-\theta_{23})
ambiguity (which can be resolved at a neutrino factory) and a residual (\delta,
\pi-\delta) ambiguity. However, whether or not CP violation occurs in the
neutrino sector can be ascertained independently of the latter two ambiguities.
The (\delta,\pi-\delta) ambiguity can be eliminated by performing a second
measurement to which only the \cos\delta terms contribute. The hierarchy of
mass eigenstates can be determined at other oscillation peaks only in the most
optimistic conditions, making it necessary to use the first oscillation
maximum. We show that the degeneracies may severely compromise the ability of
the proposed SuperJHF-HyperKamiokande experiment to establish CP violation. In
our calculations we use approximate analytic expressions for oscillation
probabilitites that agree with numerical solutions with a realistic Earth
density profile.
