We need to simplify the initial expression as follows
[tex]\begin{gathered} \csc (-660degree) \\ =\frac{1}{\sin(-660degree)} \\ =\frac{1}{\sin(-300-360degree)} \\ =\frac{1}{\sin(-300degree)} \\ =-\frac{1}{\sin(300degree)} \end{gathered}[/tex]Then, in a diagram
The blue angle is a 300°, then we found out that sin(300°)= -sin(60°), as shown in the figure
Then
[tex]\begin{gathered} -\frac{1}{\sin(300degree)}=\frac{1}{\sin (60\text{degre}e)} \\ \Rightarrow\csc (-660degree)=\frac{1}{\sin (60degree)} \end{gathered}[/tex]Therefore, the coterminal angle is +60°
