The value of $$\begin{aligned} \cos \left(18^{\circ}-\mathrm{A}\right) \cdot \cos ( & \left.18^{\circ}+\mathrm{A}\right) \\ & -\cos \left(72^{\circ}-\mathrm{A}\right) \cos \left(72^{\circ}+\mathrm{A}\right) \text { is }\end{aligned}$$

$$\cos ^2 48^{\circ}-\sin ^2 12^{\circ}=$$ _________, if $$\sin 18^{\circ}=\frac{\sqrt{5}-1}{4}$$

If $$\tan \theta=\frac{\sin \alpha-\cos \alpha}{\sin \alpha+\cos \alpha}, 0 \leq \alpha \leq \frac{\pi}{2}$$, then the value of $$\cos 2 \theta$$ is

The value of $$\tan \left(\frac{\pi}{8}\right)$$ is _________.