If $${\text{2}}\sin \theta + {\text{cos}}\theta = \frac{7}{3}{\text{,}}$$    then the value of $$\left( {{\text{ta}}{{\text{n}}^2}\theta - {{\sec }^2}\theta } \right)$$   is?

Solution (By Examveda Team)

$$\eqalign{ & {\text{2}}\sin \theta + {\text{cos}}\theta = \frac{7}{3} \cr & \Rightarrow \left( {{\text{ta}}{{\text{n}}^2}\theta - {\text{se}}{{\text{c}}^2}\theta } \right) \cr & \Rightarrow \left( {{{\sec }^2}\theta - 1 - {\text{se}}{{\text{c}}^2}\theta } \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\left[ {\because 1 + {\text{ta}}{{\text{n}}^2}\theta = {{\sec }^2}\theta } \right] \cr & \Rightarrow - 1 \cr} $$