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In the context of neutrino factories, we review the solution of thedegeneracies in the neutrino oscillation parameters. In particular, we have setlimits to $\sin^2 2\theta_{13}$ in order to accomplish the unambiguousdetermination of $\theta_{23}$ and $\delta$. We have performed two differentanalysis. In the first, at a baseline of 3000 km, we simulate a measurement ofthe channels $\nu_e\to\nu_\mu$, $\nu_e\to\nu_\tau$ and$\bar{\nu}_\mu\to\bar{\nu}_\mu$, combined with their respective conjugate ones,with a muon energy of 50 GeV and a running time of five years. In the second,we merge the simulated data obtained at L=3000 km with the measurement of$\nu_e\to\nu_\mu$ channel at 7250 km, the so called 'magic baseline'. In bothcases, we have studied the impact of varying the $\nu_\tau$ detectorefficiency-mass product, $(\epsilon_{\nu_\tau}\times M_\tau)$, at 3000 km,keeping unchanged the $\nu_\mu$ detector mass and its efficiency. At L=3000 km,we found the existance of degenerate zones, that corresponds to values of$\theta_{13}$, which are equal or almost equal to the true ones. These zonesare extremely difficult to discard, even when we increase the number of events.However, in the second scenario, this difficulty is overcomed, demostrating therelevance of the 'magic baseline'. From this scenario, the best limits of$\sin^2 2\theta_{13}$, reached at $3\sigma$, for $\sin^2 2\theta_{23}=0.95$,0.975 and 0.99 are: 0.008, 0.015 and 0.045, respectively, obtained at$\delta=0$, and considering $(\epsilon_{\nu_\tau}\times M_\tau) \approx 125$,which is five times the initial efficiency-mass combination.Comment: 40 pages, 18 figures; added references, corrected typos, updated Eq  (15c

Revising the solution of the neutrino oscillation parameter degeneracies at neutrino factories