Sleeping Beauty problem

Sleeping Beauty agrees to take part in an experiment in which the following things take place.

Sunday:
Researchers give Sleeping Beauty a drug that puts her to sleep. They then flip a fair coin.

Monday:
Sleeping Beauty is woken up. She is then adminisered a memory-erasing drug and put back to sleep, (without any memory of being awakened).

Tuesday:
If the coin flip came up tails, Sleeping Beauty is woken up again, and again put back to sleep.

Wednesday:
Sleeping Beauty is woken up, and the experiment is over.

When Sleeping Beauty is woken up for the first time, what should her degree of belief be (as a fraction) that the coin toss came up heads?

(If you care, you can check out current opinion on the answer here, and here, and finally here.)