If $0 < B < A < \frac{\pi}{4}, \cos ^{2} B-\sin ^{2} A=\frac{\sqrt{3}+1}{4 \sqrt{2}}$ and $2 \cos A \cos B=\frac{1+\sqrt{2}+\sqrt{3}}{2 \sqrt{2}}$, then $\cos ^{2} \frac{4 B}{3}-\sin ^{2} \frac{4 A}{5}=$

If $\theta$ is an acute angle and $2 \sin ^{2} \theta=\cos ^{4} \frac{\pi}{8}+\sin ^{4} \frac{3 \pi}{8}+\cos ^{4} \frac{5 \pi}{8}+\sin ^{4} \frac{7 \pi}{8}$, then $\theta=$

If $2 \tan ^{2} \theta-4 \sec \theta+3=0$, then $2 \sec \theta=$

If $0 < \theta < \frac{\pi}{4}$ and $8 \cos \theta+15 \sin \theta=15$, then $15 \cos \theta-8 \sin \theta=$