Answer
$\dfrac {2\cos \theta \times\tan \left( \sin \theta \right) }{\cos ^{2}\left( \sin \theta \right) }$
Work Step by Step
$\dfrac {d}{d\theta }\left( \tan ^{2}\left( \sin \theta \right) \right) =2\tan \left( \sin \theta \right) \times \left( \dfrac {d}{d\theta }\tan \left( \sin \theta \right) \right) =\dfrac {2\tan \left( \sin \theta \right) }{\cos ^{2}\left( \sin \theta \right) }\times \left( \dfrac {d}{d\theta }\left( \sin \theta \right) \right) =\dfrac {2\cos \theta \times\tan \left( \sin \theta \right) }{\cos ^{2}\left( \sin \theta \right) }$
