If tan 7θ tan 2θ = 1, then the value of tan 3θ is

tan 7θ . tan 2θ = 1

$\Rightarrow \tan 7 \theta=\frac{1}{\tan 2 \theta}=\cot 2 \theta$

$\Rightarrow \tan 7 \theta=\tan \left(90^{\circ}-2 \theta\right)$

$\Rightarrow 7 \theta=90^{\circ}-2 \theta$

$\Rightarrow 9 \theta=90^{\circ} \Rightarrow \theta=10^{\circ}$

$\therefore \tan 3 \theta=\tan 30^{\circ}=\frac{1}{\sqrt{3}}$