  Seesaw mechanism constrains from below mixing between active and sterile
neutrinos for fixed sterile neutrino masses. Signal events associated with
sterile neutrino decays inside a detector at fixed target experiment are
suppressed by the mixing angle to the power of four. Therefore sensitivity of
experiments such as SHiP and DUNE should take into account minimal possible
values of the mixing angles. We extend the previous study of this subject
arXiv:1312.2887 to a more general case of non-zero CP-violating phases in the
neutrino sector. Namely, we provide numerical estimate of minimal value of
mixing angles between active neutrinos and two sterile neutrinos with the third
sterile neutrino playing no noticeable role in the mixing. Thus we obtain a
sensitivity needed to fully explore the seesaw type I mechanism for sterile
neutrinos with masses below 2 GeV, and one undetectable sterile neutrino that
is relevant for the fixed-target experiments. Remarkably, we observe a strong
dependence of this result on the lightest active neutrino mass and the neutrino
mass hierarchy, not only on the values of CP-violating phases themselves. All
these effects sum up to push the limit of experimental confirmation of
sterile-active neutrino mixing by several orders of magnitude below the results
of arXiv:1312.2887 from $10^{-10}$ - $10^{-11}$ down to $10^{-12}$ and even to
$10^{-20}$ in parts of parameter space; nonzero CP-violating phases are
responsible for that.
