Explanation

Multiply the first fraction's numerator and denominator by (sinθ + cosθ + 1); it simplifies to 1/(sinθcosθ) + 1/cosθ − cosθ/sinθ. Subtracting (sinθ + 1)/cosθ leaves (1 − cos²θ − sin²θ)/(sinθcosθ) = 0. The final numerator 1 − sin²θ − cos²θ vanishes identically, giving 0.