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Solving the ArcTan of an angle (Radians) by hand? Converting to radians gives $\mathrm {arctan} (1)=\pi 4$ Finding the exact arctangent of other values would be much more complicated, though you ought to be able to estimate the arctangent by picturing it
real analysis - $\arctan (x) + \arctan (1 x) = \frac {\pi} {2 . . . $$\theta +\phi =\arctan (x)+\arctan (1 x)=\pi 2$$ While in this development, the angles were restricted to be between $0$ and $\pi 2$, we can adapt this same approach show that the relationship is indeed general for $x>0$
Find the value of $\arctan (1 3)$ - Mathematics Stack Exchange That is because the answer is not some nice rational fraction times $\pi$ Of course, you can look up (or use a calculator) to determine the $\arctan (1 3)$ (which equals $0 322$ radians or $18 435^\circ$ ) and then divide by $\pi$, but I don't think that is what you are looking for! There is a way to represent the $\arctan$ using the series: