Let S be the set of all complex numbers z satisfying $|\mathrm{z}-2+\mathrm{i}|\ge \sqrt{5}$. If the complex number z₀ is such that $\frac{1}{|{\mathrm{z}}_0-1|}$ is the maximum of the set $\{\frac{1}{|\mathrm{z}-1|}:\mathrm{z}\in \mathrm{S}\}$, then the principal argument of $\frac{4-{\mathrm{z}}_0-{\overline{\mathrm{z}}}_0}{{\mathrm{z}}_0-{\overline{\mathrm{z}}}_0+2\mathrm{i}}$ is