I can do an fft of a voice/audio signal and get the different phases, intensity's, and frequencies accurately. What I'm trying to understand is why do certain values for the phase angle become greater than 2pi or less than -2pi? I know I can do a modulo of the phase angle so it doesn't go past 2pi or -2pi but I'm trying to understand why I can get a phase angle of -1343 radians or 234 radians and if there is another meaning to having such large phase angles.
An Example would be quaternions which deals with higher dimensional math do we arbitrarily ignore something by not taking into account such large negative and positive phase angle values?
Unwrapped phase angles of an FT spectrum are useful if you are trying to plot or analyse a continuous phase change over time (frequency modulation, etc.) or over frequency (multi-pole filter response, phase vocoder or cepstrum/cepstral analysis or synthesis), without jump discontinuities over time, frequency or quefrency, which could ruin linear operations, plot slope regression, and etc.