  We re-fit for the neutrino mass-squared difference $\Delta m^2$ in the
threefold maximal (ie. tri-maximal) mixing scenario using recent CHOOZ and
SUPER-K data, taking account of matter effects in the Earth. While matter
effects have little influence on reactor experiments and proposed long-baseline
accelerator experiments with $L \simlt 1000 km$, they are highly significant
for atmospheric experiments, suppressing naturally $\nu_e$ mixing and enhancing
$\nu_{\mu} - \nu_{\tau}$ mixing, so as to effectively remove the experimental
distinction between threefold maximal and twofold maximal
$\nu_{\mu}-\nu_{\tau}$ mixing. Threefold maximal mixing is fully consistent
with the CHOOZ and SUPER-K data and the best-fit value for the neutrino
mass-squared difference is $\Delta m^2 = (0.98 \pm^{0.30}_{0.23}) \times
10^{-3} eV^2$.
