Answer
$2\tan \theta $
Work Step by Step
$\dfrac {\left( sec\theta -\tan \theta \right) ^{2}+1}{sec\theta csc\theta -\tan \theta csc\theta }=\dfrac {\left( \dfrac {1-\sin \theta }{\cos \theta }\right) ^{2}+1}{\dfrac {1}{\cos \theta }\dfrac {1}{\sin \theta }-\dfrac {1}{\cos \theta }}=\dfrac {\dfrac {1-2\sin \theta +\sin ^{2}\theta +\cos ^{2}\theta }{\cos ^{2}\theta }}{\dfrac {1}{\cos \theta }\left( \dfrac {1}{\sin \theta }-1\right) }=$
$\dfrac {2\left( 1-\sin \theta \right) }{\cos \theta \dfrac {\left( 1-\sin \theta \right) }{\sin \theta }}=2\tan \theta $
