I'm getting spoonfed instructions and I still don't get it. >_>

I am to find the inverse of f(x) = x^3 + x, by using properties of sinh(x).

The question tells me to let y = x^3 + x, let z =

and then prove that

.

After I do that, it tells me to set z = sinh(θ), solve for θ and then reverse the changes to the variables to find x as a function of y.

I managed to do most of it, up until the 'reverse the changes' part. My θ equals something ridiculously long and confusing, and I have no idea how to use it to my benefit.

Just need a bit of guiding light, it feels like I overlooked something...

EDIT: All right, well, I solved for θ in terms of x now too.

And then I equate the two.

And I'm not exactly sure how to solve...