Practical zero-phase filters are zero-phase in their passbands, but may switch between 0 and in their stopbands (as illustrated in the upcoming example of Fig.10.2). Thus, typical zero-phase filters are more precisely described as piecewise constant-phase filters, where the constant phase is 0 in all passbands, and over various intervals within stopbands. Similarly, practical ``linear phase'' filters are typically truly linear phase across their passbands, but typically exhibit discontinuities by radians in their stopband(s). As long as the stopbands are negligible, which is the goal by definition, the -phase regions can be neglected completely.
Trigonometric Identities, Continued