$$\frac{1}{\sqrt{2}}\times\frac{\sqrt{3}}{2}+\frac{1}{\sqrt{2}}\times\frac{1}{2}$$
$\frac{\sqrt{2}\left(\sqrt{3}+1\right)}{4}\approx 0.965925826$
$$\frac{\sqrt{2}}{\left(\sqrt{2}\right)^{2}}\times \frac{\sqrt{3}}{2}+\frac{1}{\sqrt{2}}\times \frac{1}{2}$$
$$\frac{\sqrt{2}}{2}\times \frac{\sqrt{3}}{2}+\frac{1}{\sqrt{2}}\times \frac{1}{2}$$
$$\frac{\sqrt{2}\sqrt{3}}{2\times 2}+\frac{1}{\sqrt{2}}\times \frac{1}{2}$$
$$\frac{\sqrt{2}\sqrt{3}}{2\times 2}+\frac{\sqrt{2}}{\left(\sqrt{2}\right)^{2}}\times \frac{1}{2}$$
$$\frac{\sqrt{2}\sqrt{3}}{2\times 2}+\frac{\sqrt{2}}{2}\times \frac{1}{2}$$
$$\frac{\sqrt{2}\sqrt{3}}{2\times 2}+\frac{\sqrt{2}}{2\times 2}$$
$$\frac{\sqrt{2}\sqrt{3}+\sqrt{2}}{2\times 2}$$
$$\frac{\sqrt{6}+\sqrt{2}}{2\times 2}$$
$$\frac{\sqrt{6}+\sqrt{2}}{4}$$
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$\frac{\sqrt{2} {(\sqrt{3} + 1)}}{4} = 0.9659258262890683$
