Answer
See below.
Work Step by Step
$LHS=\frac{cot\theta}{1-tan\theta}+\frac{tan\theta}{1-cot\theta}=\frac{cos^2\theta}{sin\theta(cos\theta-sin\theta)}+\frac{sin^2\theta}{cos\theta(sin\theta-cos\theta)}=\frac{cos^3\theta-sin^3\theta}{sin\theta cos\theta(cos\theta-sin\theta)}=\frac{cos^2\theta+sin^2\theta+sin\theta cos\theta}{sin\theta cos\theta}=cot\theta+tan\theta+1=RHS$
