If a rectangular area is rotated in a uniform electric field from the position where the maximum electric flux goes through it to an orientation where only half the flux goes through it, what has been the angle of rotation?

With a uniform electric field, flux go along parallel paths, then flux is therefore proportional to the cosine of the angle rotated.

0 degree rotation = > cos (0) = 1 = > 100% of flux.

60 degrees rotation = > cos (60) = > 0.5 = > how many % of flux?