[math-fun] PhudgIng phi

What is the small but non-zero angle of tangency between the golden spiral and the associated nest of golden rectangles? And does this angle occur elsewhere in geometry? (Lots of phi-fans pretend the angle is zero; hence the title of this post.) See https://books.google.com/books?id=Gw-lqvE6fNgC&pg=PT102&lpg=PT102&dq=golden+... Jim Propp