Frequency response of H(jω)=13(1+e−jω+e−j2ω){\displaystyle H(j\omega )={\frac {1}{3}}\left(1+e^{-j\omega }+e^{-j2\omega }\right)}. The top plot is the magnitude plot and the bottom plot is the phase plot.  At the two frequencies where the magnitude goes to zero, there is a sign reversal which causes the phase discontinuities by π radians.  Thus they are true discontinuities, not artifacts of phase wrapping.
Own work
Krishnavedala