Answer
$\csc 166.7^{\circ}$ = 4.3469
Work Step by Step
Using calculator in degree mode-
166.7 → $\sin$ → $\frac{1}{x}$ (Recall $\csc\theta$ = $\frac{1}{\sin\theta}$)
$\csc 166.7^{\circ}$ = 4.3468860787
Rounding it to four places past the decimal point-
$\csc 166.7^{\circ}$ = 4.3469