이항계수 합과 탄젠트

$f ( x ) = _{6} C _{0} + _{6} C _{1} x ^{2} + _{6} C _{2} x ^{4} + _{6} C _{3} x ^{6} + _{6} C _{4} x ^{8}$ $+ _{6} C _{5} x ^{10} + _{6} C _{6} x ^{12}$ $\displaystyle = \sum\limits _{{k} = 0} ^{6} {}_{6} \mathrm{C} _{k} x ^{2k} = ( 1 + x ^{2} ) ^{6}$ $f ( \tan \theta ) = ( 1 + \tan ^{2} \theta ) ^{6} = 2 ^{12}$ $1 + \tan ^{2} \theta = 4$ $\leftrightarrow$ $\tan ^{2} \theta = 3$ $\leftrightarrow$ $\displaystyle \tan \theta = \sqrt{3}$ ( $\displaystyle \because 0 < \theta < \frac{\pi}{2}$에서 $\tan \theta > 0$) $\therefore$ $\displaystyle \theta = \frac{\pi}{3}$ 이므로 $\displaystyle \frac{36 \theta}{\pi} = 12$