  We consider the interplay of fundamental and matter-induced T violation
effects in neutrino oscillations in matter. After discussing the general
features of these effects we derive a simple approximate analytic expression
for the T-violating probability asymmetry \Delta P^T_{ab} for three-flavour
neutrino oscillations in a matter with an arbitrary density profile in terms of
the two-flavour neutrino amplitudes. Explicit examples are given for the cases
of a two-layer medium and for the adiabatic limit in the general case. We then
discuss implications of the obtained results for long baseline experiments. We
show, in particular, that asymmetric matter effects cannot hinder the
determination of the fundamental CP and T-violating phase \delta_{CP} in the
long baseline experiments as far as the error in this determination is larger
than 1% at 99% C.L. Since there are no T-violating effects in the two-flavour
case, and in the limits of vanishing \theta_{13} or \Delta m_{21}^2 the
three-flavour neutrino oscillations effectively reduce to the two-flavour ones,
studying the T-violating asymmetries \Delta P^T_{ab} can in principle provide
us with a complementary means of measuring \theta_{13} and \Delta m_{21}^2.
