Answer
$-\sec\theta $
Work Step by Step
$\dfrac {csc\theta }{\cot \left( -\theta \right) }=\dfrac {1}{\dfrac {\sin \theta \cos \left( -\theta \right) }{\sin \left( -\theta \right) }}=\dfrac {-\sin \theta }{\sin \theta \cos \theta }=-\dfrac {1}{\cos \theta }=-sec\theta $
