Sample size formula for comparing more than 2 proportions

Question

I have one control group and two treatment groups.

I know the sample size formulae for comparing two proportions.

n = (Zα/2+Zβ)2 * (p1(1-p1)+p2(1-p2)) / (p1-p2)2,

Can someone please help me what the formula should be for comparing 3 proportions?

Thanks