If $$\cos \theta=-\sqrt{\frac{3}{2}}$$ and $$\sin \alpha=\frac{-3}{5}$$, where '$$\theta$$' does not lie in the third quadrant, then the value of $$\frac{2 \tan \alpha+\sqrt{3} \tan \theta}{\cot ^2 \theta+\cos \alpha}$$ is equal to

If $$\tan \beta=\frac{\tan \alpha+\tan \gamma}{1+\tan \alpha \tan \gamma}$$, then $$\frac{\sin 2 \alpha+\sin 2 \gamma}{1+\sin 2 \alpha \sin 2 \gamma}$$ is equal to

The sides of a triangle inscribed in a given circle subtend angles $$\alpha, \beta, \gamma$$ at the center. The minimum value of the AM of $$\cos \left(\alpha+\frac{\pi}{2}\right), \cos \left(\beta+\frac{\pi}{2}\right)$$ and $$\cos \left(\gamma+\frac{\pi}{2}\right)$$ is equal to

In a $$\triangle A B C$$, if $$3 \sin A+4 \cos B=6$$ and $$4 \sin B+3 \cos A=1$$, then $$\sin (A+B)$$ is equal to