Answer
The equation is an identity.
Please see proof in "step-by-step"
Work Step by Step
With
$\displaystyle \csc\theta=\frac{1}{\sin\theta},\quad$and $\sin(-\theta)=-\sin\theta$
$ LHS=\displaystyle \frac{1}{\sin\theta}-\sin\theta,\quad$
... common denominator is $\sin \theta$
$LHS=\displaystyle \frac{1-\sin^{2}\theta}{\sin\theta}$
in the numerator, apply the Pythagorean identity
$\cos^{2}\theta+\sin^{2}\theta=1$
$LHS=\displaystyle \frac{\cos^{2}\theta+\sin^{2}\theta-\sin^{2}\theta}{\sin\theta}=\frac{\cos^{2}\theta}{\sin\theta}=RHS$
