What is the value of $$\sin \left( {180 - \theta } \right)\sin \left( {90 - \theta } \right) + \frac{{\cot \left( {90 - \theta } \right)}}{{1 + {{\tan }^2}\theta }}?$$

$$\eqalign{ & \sin \left( {180 - \theta } \right)\sin \left( {90 - \theta } \right) + \frac{{\cot \left( {90 - \theta } \right)}}{{1 + {{\tan }^2}\theta }} \cr & \Rightarrow \sin \theta \cos \theta + \frac{{\tan \theta }}{{{{\sec }^2}\theta }} \cr & \Rightarrow \sin \theta \cos \theta + \frac{{\sin \theta }}{{\cos \theta }} \times {\cos ^2}\theta \cr & \Rightarrow \sin \theta \cos \theta + \sin \theta \cos \theta \cr & \Rightarrow 2\cos \theta \sin \theta \cr} $$