Draw an equilateral triangle of side length 2 sitting on its base.
Split it down the middle.
You now have a 60/30/90 triangle. The base is 1 (half of the original 2), the hypotenuse is 2 (the original side). Pythagoras's rule says the other side is sqrt(3).
Remember that 30 degrees is pi/6 radians.
Use tan A = opp/adj to get tan (pi/6) = 1/sqrt(3).
Rationalise the denominator of this fraction by mutiplying top and bottom by sqrt(3) to get....voila.... sqrt(3) / 3.