Nonvanishing section for direct sum of Mobius band
For a direct sum of Mobius band, it is trivial if it has two linear independent nonvanishing sections. I have the following as my sections：
s1=(E^(i*theta), (Cos(theta/2), Sin(theta/2))
s2=(E^(i*theta), (-Sin(theta/2), Cos(theta/2))
Clearly, the above sections are linearly independent and nonvanishing, but I am not sure if they are indeed the correct ones, need help to confirm!