Not the best at explaining things but here goes:
First use the unit circle to find all angles in which sine equals 1/2 and write them down in radians.
Sine works with the interval equation angle + 2*pi*k
Since it is double angle (sine2theta) you must use the equation for both of the radians you wrote down before and divide by 2 to get your formulas.
You then plug in numbers to K to find all occurrences where theta equals anything in the interval 0 to 2pi
sin2theta = 1/2
2theta = pi/6 , 5pi/6
2theta = pi/6 + 2*pi*k
theta = pi/12 + pi*k
2theta = 5pi/6 + 2*pi*k
theta = 5pi/12 + pi*k
Try plugging in 0,1,2,3 and so on to both equations and your answer will be all the numbers that are between your interval of 0 and 2pi.
Hope that helps somewhat, but I'm sure someone else can explain it much better.