Given positive integers $m<n\in\mathbb{N}$ is there an algorithm to find integers $z_1, z_2\in \mathbb{Z}\setminus\{0\}$ such that $\frac{m}{n}$ is best approximated by $\frac{1}{z_1}+\frac{1}{z_2}$? (In other words, the goal is to minimize $|\frac{m}{n}- (\frac{1}{z_1}+\frac{1}{z_2})|$.)