8.24x10^-5 rad/sec
The key thing to remember for this problem is that in the process of orbiting its parent star, the planet will rotate one more time than the number of days the planet sees as it's year. For instance, on Earth, a day is 24 hours, or 1440 minutes long. But the sidereal day (how long the Earth takes to rotate about it's axis as referenced to distant stars) is about 4 minutes shorter. And if you take 1440 and divide by 365.2425, you'll get 3.9 minutes or "about 4 minutes". So let's calculate how many times the observed planet rotates.
59.1 days/year * 24 hours/day = 1418.4 hours/year
Since the planet has a "day" of 21.5 hours, that means that the planet experiences 1418.4/21.5 = 65.97 days per year. Add the extra rotation needed and the planet turns on its axis 66.97 times per local year.
Now, divide by the length of its year to get the number of rotations per earth day
66.97/59.1 = 1.133164129 rotations per 24 hours.
Convert from rotations to radians.
1.133164129 * 2 * pi = 7.119880203 rad
Now divide by the number of seconds in a day (24*60*60 = 86400)
7.119880203 rad / 86400 sec = 8.2406x10^-5 rad/sec
Rounding to 3 significant figures gives 8.24x10^-5 rad/sec
