 Solution

Neglecting intersite orbital overlap, one normalized real set of symmetry-adapted linear combinations isThe coefficient vectors are orthonormal. The first has equal phase at all three sites; the second opposes site $A$ to $B,C$; the third has zero amplitude at $A$ and opposite phases at $B,C$. Any orthonormal rotation of the two $E$ functions is equally valid. With nonzero intersite orbital overlap, normalization must instead use the overlap matrix.