  For any three element set of positive integers, $\{a,b,n\}$, with $a<b<n$,
$n$ sufficiently large and $\gcd(a,b)=1$, we find the least $\alpha$ such that
given any real numbers $t_1$, $t_2$, $t_3$, there is a real number $x$ such
that \begin{equation*} \max \{\left\langle ax-t_{1}\right\rangle ,\left\langle
bx-t_{2}\right\rangle ,\left\langle nx-t_{3}\right\rangle \}\leq \alpha ,
\end{equation*} where $\left\langle \cdot \right\rangle $ denotes the distance
to the nearest integer. The number $\alpha $ is known as the angular Kronecker
constant of $\{a,b,n\}$. We also find the least $\beta $ such that the same
inequality holds with upper bound $\beta $ when we consider only approximating
$t_{1},t_{2},t_{3}$ $\in \{0,1/2\}$, the so-called binary Kronecker constant.
The answers are complicated and depend on the congruence of $n\mod(a+b)$.
Surprisingly, the angular and binary Kronecker constants agree except if
$n\equiv a^{2}\mod(a+b)$.
