If I purchase a share of stock for $10, sell it for $9, repurchase it less than 30 days later for $8, and sell it for $9 before the end of the year, will my gain be zero?

Yes, that's right. The first sale is a wash sale, so the $1 loss is disallowed, but it is added to the basis of the replacement share. So the basis of the replacement share is the $8 that you paid for it plus the $1 disallowed loss from the wash sale, which is $9. You sold it for $9 so you have no gain or loss.

This works only if you then stop trading that security for the required interval, otherwise, wash sales can perpetuate.

@mtg1909 

Right - thank you!