Solution
= Solution
The left side of the stated identity must inherit $R_{abcd}=-R_{abdc}$. Exchange $c$ and $d$, reduce all curvature products using pair antisymmetry and the first Bianchi identity, and compare with the negative of the original expression. The unmatched mixed products cancel precisely for
$$
\boxed{\alpha=2}.
$$
This is the coefficient appearing in the <Penrose wave equation> with the curvature convention of part a.