Phase Spectrum in Fourier Transform
I think that the plot you display does not show the correct answer, what makes me think that is that you inject in your fft a pure sinewave with an initial phase equal to 0. Therefore your plot should display a 0 phase shift for every frequency bins.
For exemple, below you can see the phase plot of a pure sine wave with an initial phase shift of 30 degrees.

The phase spectrum will be here to tell you in which way your signals are delayed for each frequency components.