$$\frac{ \tan 45 }{ \tan 30+ \tan 60 }$$
$\frac{\sqrt{3}}{4}\approx 0.433012702$
$$\frac{1}{\tan(30)+\tan(60)}$$
$$\frac{1}{\frac{\sqrt{3}}{3}+\tan(60)}$$
$$\frac{1}{\frac{\sqrt{3}}{3}+\sqrt{3}}$$
$$\frac{1}{\frac{4}{3}\sqrt{3}}$$
$$\frac{\sqrt{3}}{\frac{4}{3}\left(\sqrt{3}\right)^{2}}$$
$$\frac{\sqrt{3}}{\frac{4}{3}\times 3}$$
$$\frac{\sqrt{3}}{4}$$
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