I haven't read the book, but have heard of such solutions.
Basically: given that anxiety about sleeping prevents sleeping, the solution is necessarily to remove anxiety about sleeping. How? By realizing that peaceful rest, while awake, is also restful, and will suffice. So spend the time in bed peacefully resting and if that happens all night, it'll do.
Anecdotally, I have had extreme insomnia, not sleeping for days in a row, at the times in my life when I had the most extreme anxiety, and when the anxiety was removed it went away instantly.
