Answer
$\cot 420^{\circ}$ = 0.5774
Work Step by Step
Using calculator in degree mode-
420 → $\tan$ → $\frac{1}{x}$ (Recall $\cot\theta$ = $\frac{1}{\tan\theta}$)
$\cot 420^{\circ}$ = 0.5773502692
Rounding it to four places past the decimal point-
$\cot 420^{\circ}$ = 0.5774