Is there a approximation error in the fisheye camera model

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At https://docs.opencv.org/master/db/d58/group__calib3d__fisheye.html, it says

If the fisheye distortion is and only is changing theta to theta_d, and after the distortion, use pinhole projection, then a more reasonable formula is

That is, tan(theta_d) should be used instead of theta_d to calculate x' and y'.

Is this a approximation error here?