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