For every angle θ at which both sides are defined, cotθ − tanθ is equal to:

Over a common denominator, cotθ − tanθ = (co$s^2$θ − si$n^2$θ)/(sinθ·cosθ) = cos2θ ÷ ((1/2)sin2θ) = 2cot2θ. The factor 2 comes from sinθ·cosθ being only half of sin2θ — dropping it leaves the trap cot2θ. Check at θ = 30°: 1.7321 − 0.5774 = 1.1547 = 2cot60°.