At pi/2 that approximation gets you 1.0045, i.e. half a percent off, so it's not particularly good at that. (still could be sufficient for some uses though; but

At pi/2 that approximation gets you 1.0045, i.e. half a percent off, so it's not particularly good at that. (still could be sufficient for some uses though; but not the best achievable even with that performance)