Why unpolarized light from a source does not show a variation in intensity when viewed through a polaroid which is rotated?

An unpolarized light wave has direction of vibration of electric field in all directions. When an unpolarized light is passed through a polaroid, output light wave is polarized in only one direction along the polaroid. As the polaroid is rotated, the intensity does not change as the original light wave has symmetric electric field in all directions. The attached figure shows the polarisation of sunlight by scattering from air molecules.
(b)Output from polaroid 2 is given by:
I2=Iocos2(60)
I2=Io/4
When polaroid 3 is rotated by an angle of 30o with respect to polaroid 2, final angle between polaroid 2 and polaroid 3 is equal to 60o. Then, intensity seen by O is:
I3=I2cos2(60)
I3=Io/16
When polaroid 3 is rotated by an angle of 60o with respect to polaroid 2, final angle between polaroid 2 and polaroid 3 is equal to 90o. Then, intensity seen by O is:
I3=I2cos2(90)
I3=0