We reconsider the extrinsic and possible intrinsic CPT violation in neutrino oscillations, and point out an identity, i.e., A(alpha beta)(CP) = A(beta alpha)(CPT) + A(alpha beta)(T), among the CP, T, and CPT asymmetries in oscillations. For three-flavor oscillations in matter of constant density, the extrinsic CPT asymmetries A(ee)(CPT), A(e mu)(CPT), A(mu e)(CPT), and A(mu mu)(CPT) caused by Earth matter effects have been calculated in the plane of different neutrino energies and baseline lengths. It is found that two analytical conditions can be implemented to describe the main structure of the contours of vanishing extrinsic CPT asymmetries. Finally, without assuming intrinsic CPT symmetry in the neutrino sector, we investigate the possibility to constrain the difference of the neutrino CF-violating phase and the antineutrino one (delta) over bar using a low-energy neutrino factory and the super-beam experiment ESS nu SB. We find that \delta - (delta) over bar\ less than or similar to 0.35 pi in the former case and \delta - (delta) over bar\ less than or similar to 0.7 pi in the latter case can be achieved at the 3 sigma confidence level if delta = (delta) over bar = pi/2 is assumed. (C) 2015 The Authors. Published by Elsevier B.V.