Hello there, it is sufficient for part b) just to check that the LHS and the RHS agree. So considered separately, when theta=180 , the LHS sin(360)=0 and the RHS 2-2cos(360) = 0. This shows that theta=180 is a solution; therefore, there is no need for arrangement.
For part c), I think you have a made a small mistake when rearranging - it should be 1= (2-2 cos(2 theta)) / ( sin 2 theta) which gives tan theta = 0.5.
Hope this is helpful