If = 1, = 1 , then the value of \ 3 ( 2/3 ) + 1 \ is?

Answer: Option C

$$\begin{array}{rl}& \pi \sin \theta =1.....(i)\\ & \pi \cos \theta =1.....(ii)\\ & \text{Divide eq}\text{. (i) from (ii)}\\ & \frac{\pi \sin \theta }{\pi \cos \theta }=\frac{1}{1}\\ & \tan \theta =1\\ & \tan \theta =\tan 45^{\circ }\\ & \theta =45^{\circ }\\ & \therefore \sqrt{3}\tan \left(\frac{2}{3}\theta \right)+1\\ & =\sqrt{3}\tan \left(\frac{2}{3}\times {45}^{\circ }\right)+1\\ & =\sqrt{3}\text{ tan}30^{\circ }+1\\ & =\sqrt{3}\times \frac{1}{\sqrt{3}}+1\\ & =2\end{array}$$