How do you evaluate csc^-1(-1) without a calculator?

##csc^-1 (-1)=-pi/2##.
Recall the Defn. of ##csc^-1## function :
##csc^-1 x=theta |x| ge 1 iff csc theta=x theta in [-pi/2pi/2]-{0}##.
We have ##csc(-pi/2)=-1 where -pi/2 in [-pi/2pi/2]-{0} csc^-1 (-1)=-pi/2##.