$\frac{\sqrt{3}}{16 \sqrt{2}}$

$\frac{\sqrt{3}}{8 \sqrt{2}}$

$\frac{1}{32}$

$\frac{1}{16}$

$4 \sin \left(\frac{A+B}{4}\right) \sin \left(\frac{A+C}{4}\right) \sin \left(\frac{A+D}{4}\right)$

$4 \sin \left(\frac{A+B}{2}\right) \cos \left(\frac{A+C}{4}\right) \cos \left(\frac{A+D}{4}\right)$

$4 \sin \left(\frac{A+B}{2}\right) \sin \left(\frac{A+C}{2}\right) \sin \left(\frac{A+D}{2}\right)$

$4 \sin \left(\frac{A+B}{2}\right) \sin \left(\frac{A+C}{4}\right) \sin \left(\frac{A+D}{4}\right)$

$\frac{1+\sqrt{7}}{4}$

$\frac{1-\sqrt{7}}{4}$

$\frac{4-\sqrt{7}}{3}$

$-\frac{(4+\sqrt{7})}{3}$

$\frac{4}{17}$

2

$\frac{7}{17}$

$\frac{4}{5}$