One divided by the square root of three is equal to the tangent of one third of a right angle.
At first glance, it seems a happy accident that these functions would meet at a whole integer.
But imagine an equilateral triangle with sides equal to 2. If you split the triangle in two along the central axis, the length of half the base is equal to 1. The height of the triangle is equal to √3. The top angle is 30°, from which the height is adjacent and the base is opposite. Remembering that the tangent relates the opposite side over the adjacent, this leads to the conclusion tan(30°) = 1 / √3.