Tangents of sums
Geometry
Level
3
Let \(e_k\) (for \(k = 0, 1, 2, 3, ...\)) be the \(k\)th-degree elementary symmetric polynomial in the variables
\[x_i= \tan \theta_i\]
for \(i = 0, 1, 2, \ldots\) i.e.
\[e_0 = 1\]
\[e_1 = \displaystyle \sum_i \tan \theta_i\]
\[e_2 =\displaystyle \sum_{i<j} \tan \theta_i \tan \theta_j\]
and so forth.
Find the value of
\[\tan \left( \displaystyle \sum_i \theta_i \right) .\]
by
Sharky Kesa