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**HallsofIvy** Consider an equilateral triangle with sides of length 2. All angles have measure $\displaystyle \pi/3$ radians (60 degrees). If you draw a perpendicular from one vertex to the opposite side, it bisects the opposite side and bisects the angle, giving a right triangle with hypotenuse of length 2, one leg of length 1, and so, by the Pythagorean theorem, the other leg has length $\displaystyle \sqrt{3}$. The half of the bisected angle, which is opposite the leg of length 1, has measure $\displaystyle \pi/6$ (30 degrees) so that $\displaystyle tan(\pi/6)= \frac{1}{2}$ and so $\displaystyle arctan(1/2)= \pi/6$. That is a value a math student should have memorized.