Question

A planet orbits a star once every 3.41 107 s in a nearly circular orbit of radius 1.47 1011 m.
(a) With respect to the star, determine the angular speed of the planet.

Answer 1

omega = 2*PI / T,

where
omega = your needed angular speed
T = time period (= 341107s in your example)

results in: 1.842*10^-5 radians per second


i hope you're sure, that you don't need angular velocity instead, which is another formula!