Isolate y in trigonometric equation $x = \sqrt {\csc^2(y)-1} + y \csc^2(y) $

Question

I need to isolate y in the middle of cosecants. Is there a way to continue isolating the equation?

$x= \sqrt {\csc^2(y)-1} + y \csc^2(y) $

Thanks.

Answer 1

You can't do it. That $y$ by itself makes it impossible.

Just as solving $y e^y = x$ for $y$ required the creation of a new function (Lambert W, the fearless function), so this would require the creation of a new function.