Can you combine these two formulas?

so I'm trying to make a rule that auto-colors every other category, and I came up with some formulas that work for it.

However, since I am not very familiar with countif(), I haven't been able to come up with a way to nest them.

I used:

=COUNTIF($A$2:A2,A2)

in a helper column, then:

=MOD(COUNTIF($B$2:$B2,1),2)=0

to color it in the conditional formatting. It works perfectly, but I am wondering if there's a way to do this without a helper column. I am open to revamping my formulas if there is a more efficient way to accomplish this also.