If $${\text{A}} \times {\text{tan}}\left( {\theta+ {{150}^ \circ }} \right)$$= $${\text{B}} \times \tan $$ $$\left( {\theta- {{60}^ \circ }} \right){\text{,}}$$the value of $$\frac{{{\text{A}} - {\text{B}}}}{{{\text{A}} + {\text{B}}}}$$is?

• A. $ - \frac{{\sin \theta }}{2}$$
• B. $\frac{{\sin 2\theta }}{2}$$
• C. $\frac{{\cos 2\theta }}{2}$$