= Solution
Within each pair the in-phase and out-of-phase combinations have $A_1$ and $B_1$ <symmetry> respectively. One normalized choice is
$$
\boxed{\begin{aligned}
a&=(s_1+s_2)/\sqrt2,& b&=(s_3+s_4)/\sqrt2&& (A_1),\\
c&=(s_1-s_2)/\sqrt2,& d&=(s_4-s_3)/\sqrt2&& (B_1).
\end{aligned}}
$$
The sign convention for $d$ is chosen to make the off-diagonal interaction positive in the corresponding two-by-two block. It does not change the physical predictions. These are pair <symmetry-adapted linear combinations>; the actual <molecular orbitals> are <linear combinations> within each of the two equal-symmetry pairs, found by diagonalizing the blocks.
\Image[/past-exam-of-the-chemistry-course-of-the-year-3-of-the-natural-sciences-course-of-the-university-of-cambridge/2022/paper-2b-trapezium-orbitals.png]
{title=Original normalized pair combinations used to reduce the trapezium Hamiltonian}
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