How can coherent wave not have constant phase difference

[Yinxiao Li]

One condition for wave interference is that the sources of the waves must be coherent, which means they emit identical waves with a constant phase difference.

I can understand that identical waves means they have the same wavelength. However, I don't understand what is a constant phase difference. The phase difference is always a constant, isn't it? But this definition clearly implies that it could be a non-constant.

y=A*cos(wt + theta), where theta is the initial phase.

 

[blue_leaf77]

y=A*cos(wt + theta), where theta is the initial phase.

Practical sources never behave such that $\theta$ is strictly independent of time, in reality no matter how good a source is, the condition inside the source may be changing in time, e.g. due to temperature or fluctuation in electrical power source. This leads to either small or big fluctuation of $\theta$. How big or small the initial phase fluctuates depends on the amount of how large the source is changed by whatever cause is there.