If cosθ.cosec23° = 1, the value of θ is?

Answer: Option D

$$\begin{array}{rl}& \text{cos}\theta .\text{cosec2}{\text{3}}^{\circ }=\text{1}\\ & \text{If cosA}.\text{cosecB}=\text{1}\\ & \text{Then, A + B}=90^{\circ }\\ & \text{So,}\\ & \theta \text{ + 2}{\text{3}}^{\circ }=90^{\circ }\\ & \theta =67^{\circ }\end{array}$$