$\begin{align}  & (\tan \theta +\cot \theta )\tan \theta =\left( \frac{\sin \theta }{\cos \theta }+\frac{\cos \theta }{\sin \theta } \right)\frac{\sin \theta }{\cos \theta } \\ & (\tan \theta +\cot \theta )\tan \theta =\left( \frac{{{\sin }^{2}}\theta +{{\cos }^{2}}\theta }{\sin \theta \cos \theta } \right)\times \frac{\sin \theta }{\cos \theta }\left| {{\sin }^{2}}\theta +{{\cos }^{2}}\theta =1 \right. \\ & (\tan \theta +\cot \theta )\tan \theta =\left( \frac{1}{\cos \theta } \right)\times \frac{1}{\cos \theta } \\ & (\tan \theta +\cot \theta )\tan \theta =\frac{1}{{{\cos }^{2}}\theta }={{\sec }^{2}}\theta  \\\end{align}$