Solve cot 5pi/12

Cot (5pi/12) = tan (pi/12)

tan (x/2) = (1 - cos (x)) / sin (x))

tan (pi/12) = tan ((pi/6) / 2) = (1 - cos (pi/6)) / sin (pi/6))

sin (pi/6) = 1/2

cos (pi/6) = sqrt (3) / 2

so ...

tan (pi/12) = (1 - sqrt (3) / 2) / (1/2) = 2 - sqrt (3)