  We determine the sensitivity to neutrino oscillation parameters from a study
of atmospheric neutrinos in a magnetised detector such as the ICAL at the
proposed India-based Neutrino Observatory. In such a detector that can {\em
separately} count $\nu_\mu$ and $\overline{\nu}_\mu$-induced events, the
relatively smaller (about 5\%) uncertainties on the neutrino--anti-neutrino
flux ratios translate to a constraint in the $\chi^2$ analysis that results in
a significant improvement in the precision with which neutrino oscillation
parameters such as $\sin^2\theta_{23}$ can be determined. Such an effect is
unique to all magnetisable detectors and constitutes a great advantage in
determining neutrino oscillation parameters using such detectors. Such a study
has been performed for the first time here. Along with an increase in the
kinematic range compared to earlier analyses, this results in sensitivities to
oscillation parameters in the 2--3 sector that are comparable to or better than
those from accelerator experiments where the fluxes are significantly higher.
For example, the $1\sigma$ precisions on $\sin^2\theta_{23}$ and
$|\Delta{m^2_{32(31)}}|$ achievable for 500 kTon yr exposure of ICAL are
$\sim9\%$ and $\sim2.5\%$ respectively for both normal and inverted
hierarchies. The mass hierarchy sensitivity achievable with this combination
when the true hierarchy is normal (inverted) for the same exposure is
$\Delta\chi^2\approx8.5$ ($\Delta\chi^2\approx9.5$).
