We re-fit for the neutrino mass-squared difference $��m^2$ 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 $��_e$ mixing and enhancing $��_�� - ��_��$ mixing, so as to effectively remove the experimental distinction between threefold maximal and twofold maximal $��_��-��_��$ 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 $��m^2 = (0.98 \pm^{0.30}_{0.23}) \times 10^{-3} eV^2$.

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