If tan7θ.tan2θ = 1, then the value of tan3θ is?

Answer: Option C

$$\begin{array}{rl}& \tan 7\theta .\tan 2\theta =1\\ & \left[\text{If tan A}\text{.tan B}=\text{1}\right]\\ & (\text{then, A}+\text{B}=90^{\circ })\\ & \left(7\theta +2\theta \right)=90^{\circ }\\ & 9\theta =90^{\circ }\\ & \theta =10^{\circ }\\ & \Rightarrow \tan 3\theta \\ & \Rightarrow \tan 30^{\circ }\\ & \Rightarrow \frac{1}{\sqrt{3}}\end{array}$$