If $\cos (\theta+\phi)=\frac{3}{5}$ and $\sin (\theta-\phi)=\frac{5}{13}, 0<\theta, \phi<\frac{\pi}{4}$, then $\cot (2 \theta)$ has the value

The expression $$\cos ^2 \phi+\cos ^2(\theta+\phi)-2 \cos \theta \cos \phi \cos (\theta+\phi)$$ is

If $$0< \theta<\frac{\pi}{2}$$ and $$\tan 3 \theta \neq 0$$, then $$\tan \theta+\tan 2 \theta+\tan 3 \theta=0$$ if $$\tan \theta \cdot \tan 2 \theta=\mathrm{k}$$ where $$\mathrm{k}=$$

If $$A$$ and $$B$$ are acute angles such that $$\sin A=\sin ^2 B$$ and $$2 \cos ^2 A=3 \cos ^2 B$$, then $$(A, B)=$$