Do Faraday rotation (FR) measurements have a \pi (180°) or 2\pi (360°) ambiguity?

If measurements of the orientation angle are used to calculate the rate of rotation, and the orientation angle is only defined between 0° and 180°, the FR would have a 180° ambiguity, but if it can be measure directly and the plane of polarization has rotated some multiple of 360° plus some angle, then there would be a 360° ambiguity. Is this interpretation correct?