How to convert from cosine to sin in order to find values

Hi
The question is solve each equation for x in the interval 0<x<2pi

Cot^2x-3cosecx+3=0

so far I have values for cosec as: -1 and 4

However looking at the answers it says to convert to sin you end up with sins = 1/2 or 1 but I don’t understand how they got that?

Any help would be really appreciated!! Thanks!