If tan(2θ + 45°) = cot3θ, where (2θ + 45°) and 3θ are acute angles, then the value of θ is?

Solution (By Examveda Team)

$$\eqalign{ & {\text{tan}}\left( {2\theta + {{45}^ \circ }} \right) = \cot 3\theta \cr & \left[ {{\text{If tan A}} = {\text{cot B}}} \right] \cr & ({\text{then, A}} + {\text{B}} = {90^ \circ }) \cr & \Rightarrow \left( {2\theta + {{45}^ \circ }} \right) + 3\theta = {90^ \circ } \cr & \Rightarrow 5\theta + {45^ \circ } = {90^ \circ } \cr & \Rightarrow \theta = \frac{{45}}{5} \cr & \Rightarrow \theta = {9^ \circ } \cr} $$