A sharp estimate of area for sublevel-set of Blaschke products

Let $\mathbb{D}$ be the unit disk in the complex plane. Among other results, we prove the following curious result for a finite Blaschke product: $$B(z)=e^{is}\prod _{k=1}^d\frac{z-a_k}{1-z\overline{a_k}}\mathrm{.}$$ The Lebesgue measure of the sublevel set of $B$ satisfies the following sharp inequality for $t\in [0,1]$: $$\mathrm{\mid }\{z\in \mathbb{D}:\mathrm{\mid }B(z)\mathrm{\mid }<t\}\mathrm{\mid }\le \pi t^{2\mathrm{/}d},$$ with equality at a single point $t\in (0,1)$ if and only if $a_k=0$ for every $k$. In that case the equality is attained for every $t$.