Find the value of tan π/12.

Ok, to get the answer without using a calculator, you first need to draw a right angled triangle with a 30 degree angle. Using a bit of logic and tan (30) = O/A, you will figure out that tan (30) = √3/3. tan (45) = 1, this is quite famous.

You can get the answer to tan (15) by using tan (45-30) and the trig identity (tanA-tanB) / (1+tanAtanB).

From there you can produce the result 2-√3=tan (45-30) = tan (15) = tan (π/12)

Pi/12 radians = 180/12 degrees = 15 degrees

tan (15 degrees) = 0.2679 ... (rounded)