If there's no built-in function for csc⁻¹, you can use the identity
csc⁻¹(x) = sin⁻¹(1/x)
which works because if we replace x = csc(y), for instance, we end up with
csc⁻¹(csc(y)) = sin⁻¹(1/csc(y))
and over an appropriate interval, the left side reduces to y, while 1/csc(y) = sin(y) so that the right side also reduces to sin⁻¹(sin(y)) = y.