Prove that Tan^{3}θ/( 1 + Tan^{2}θ) + Cot^{3}θ/(1 + Cot^{2}θ) = SecθCosecθ - 2SinθCosθ

Solution:

Tan^{3}θ/( 1 + Tan^{2}θ) + Cot^{3}θ/(1 + Cot^{2}θ) = SecθCosecθ - 2SinθCosθ