Pioneering atmospheric muon neutrino experiments have demonstrated the near-maximal magnitude of the flavor mixing angle \theta _ { 23 } .
But the precise value of the deviation D \equiv 1 / 2 - \sin ^ { 2 } \theta _ { 23 } from maximality ( if nonzero ) needs to be known , being of great interest – especially to builders of neutrino mass and mixing models .
We quantitatively investigate in a three generation framework the feasibility of determining D in a statistically significant manner from studies of the atmospheric \nu _ { \mu } , \bar { \nu } _ { \mu } survival probability including both vacuum oscillations and matter effects .
We show how this determination will be sharpened by considering the up-down ratios of observed \nu _ { \mu } - and \bar { \nu } _ { \mu } -induced events and the differences of these ratios in specified energy and zenith angle bins .
We consider 1 Megaton year of exposure to a magnetized iron calorimeter such as the proposed INO detector ICAL , taking into account both energy and zenith angle resolution functions .
The sensitivity of such an exposure and the dependence of the determination of D on the concerned oscillation parameters are discussed in detail .
The vital use of matter effects in fixing the octant of \theta _ { 23 } is highlighted .