= Solution
For a real nonmagnetic $T_1$ electronic triplet, the <symmetric square of a group representation> decomposes as
$$
\operatorname{Sym}^2T_1=A_1+E+T_2.
$$
The $A_1$ coordinate shifts all components equally and does not remove the degeneracy. The <linear Jahn-Teller selection rule> therefore permits \b[$E$ and $T_2$ vibrational modes] to couple and split the triplet. Both <methane> $T_2$ vibrational triplets are symmetry-eligible. A nonzero allowed coupling generally produces a symmetry-lowering instability, although symmetry alone does not determine its strength or the preferred minimum.
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