First use your calculator to find $\displaystyle{{\tan{{80}}}}^{\circ}={5.67128182}\usepackage{cmbright}\Huge\$ .

Then find the reciprocal of this: $\displaystyle{{\cot{{80}}}}^{\circ}=\frac{{1}}{{{\tan{{80}}}}^{\circ}}\text{}={0.176326981}\ldots\usepackage{cmbright}\Huge\$

Finally, round off to 0.176.