A new principle in real analysis

In 2021 we presented a principle giving bounds for the number of zeros of a given enough smooth real function f(t). Commenting this result professor H. Begehr noticed that this principle plays a role in real analysis similar to that of argument principle in the complex analysis.
In this paper we give a new version of the principle for functions f which indeed is very similar to the argument principle. The number of zeros of f are estimated by variations of some angles like in the argument principle.