For a given choice of distinct numbers $a_1,a_2\in\mathbb{D}$, there is a unique choice of real number $r\in(0,1)$ such that some degree $1$ Blaschke product maps $a_1$ to $r$ and $a_2$ to $-r$ (and that degree $1$ B-prod is unique as well).
Is there a nice formula for $r$ and $B$ in terms of $a_1$ and $a_2$? (I know how to find it typically, but my idea requires VERY messy arithmetic.)