Introductio in analysin infinitorum

AC DIVISIONE ANGULORUM. 217 & generaliter, si $n=2m$, erit CAP. XIV. $n \cdot \cot nz = -\tan z + \tan(\frac{\varpi}{n} - z) - \tan(\frac{\varpi}{n} + z) + \tan(\frac{2\varpi}{n} - z) - \tan(\frac{2\varpi}{n} + z) + \tan(\frac{3\varpi}{n} - z) - \tan(\frac{3\varpi}{n} + z) + \dots + \tan(\frac{m\varpi}{n} - z)$. 257. Per has formas iterum ambiguitas producti ex omnibus radicibus destruitur; eritque idcirco $1 = \tan z \cdot \tan(\frac{\varpi}{2} - z)$ $1 = \tan z \cdot \tan(\frac{\varpi}{4} - z) \cdot \tan(\frac{\varpi}{4} + z) \cdot \tan(\frac{2\varpi}{4} - z)$ $1 = \tan z \cdot \tan(\frac{\varpi}{6} - z) \cdot \tan(\frac{\varpi}{6} + z) \cdot \tan(\frac{2\varpi}{6} - z) \cdot \tan(\frac{2\var [TRUNCATED]