Generic initial ideals of some monomial complete intersections in four variables

Let $R=K[x_1,x_2,x_3,x_4]$ be the polynomial ring over a field of characteristic zero. For the ideal $(x_1^a,x_2^b,x_3^c,x_4^d)\subset R$, where at least one of $a$, $b$, $c$ and $d$ is equal to two, we prove that its generic initial ideal with respect to the reverse lexicographic order is the almost revlex ideal corresponding to the same Hilbert function.