Given L and E, what is the minimum Δm² that can be probed?
P(osc)=sin²2θ*sin²(1.27*Δm²[eV²]*L[km]/E[GeV])
Sensitivity is maximum when P is maximum. Given sin²2θ, P is maximum when the phase of the other sine is π/2, 3π/2, etc., i.e. (2n+1)π/2 with n=0,1,...
Phase is proportional to Δm², so we look for the minimum of the phase in this ensemble, i.e. π/2.
So, the formula for Δm² sensitivity (given θ) is (π*E)/(2*1.27*L).

Given a certain mass of the detector, a certain time (e.g. 1 year) and a certain contamination of the beam (e.g., 0.5% of ν_e in a beam of ν_μ), what is the minimum sin²2θ that can be probed?
If you take the phase = (2n+1)π/2 for the other sine (as above), this is equivalent to the minimum P.
The number of interactions (N_int) is σ(νN)*Φ(ν)[m^-2y^-1]*Δt*N_nucleons.
N_nucleons=M(detector)/m(nucleon).
Signal: S=P*N_int=sin²2θ*N_int.
Background: B=f*N_int, where f is the fraction of contamination in the beam.
Significance: S/√(B)=(P/f)*√N_int, proportional to √M(detector)
(Note: another background comes from π⁰'s from NC interactions. It can be reduced through a good angular resolution, discriminating electrons against pairs of photons.)

If background is negligible, what is the sensitivity of the experiment to sin²2θ?
As in the case above, this is equivalent to the minimum P. And the strongest limit comes from 0 events observed, so let's assume N_obs.
First, calculate the number of interactions expected in absence of oscillation.
S=P*N_int
Assume Poisson statistics: P(0,S)=e^-S
i.e. S=-log[P(0,S)]>-log(1-CL)
e.g. CL=95% (1-CL=0.05) means S>3
So the minimum P (and then the sensitivity to sin²2θ) is 3/N_int.