I have a function whose graph is as shown in the figure. I want to find where the plot starts to behave linearly.

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This is the graph of the function. X axis is an angle and y axis is the function of that angle.

This is the zoomed version of same image near origin.

As you can see in first image that the graph is linear near the center. But the zoomed image reveals that the linearity kicks in only after some value of x axis variable. Is there a way to find the exact point where linearity starts?

I have tried to solve for inflections points but it looks like the point where linearity starts is not a inflection point.