$${\left( {\frac{{1 - \tan \theta }}{{1 - \cot \theta }}} \right)^2} + 1 = ?$$

$$\eqalign{ & {\left( {\frac{{1 - \tan \theta }}{{1 - \cot \theta }}} \right)^2} + 1 \cr & = {\left( {\frac{{1 - \tan \theta }}{{\frac{{\tan \theta - 1}}{{\tan \theta }}}}} \right)^2} + 1 \cr & = \frac{{\left( {1 - \tan \theta } \right){{\tan }^2}\theta }}{{\left( {1 - \tan \theta } \right)}} + 1 \cr & = {\tan ^2}\theta + 1 \cr & = {\sec ^2}\theta \cr} $$