Math Prize 2010 Problem 15
Source:
November 14, 2010
trigonometry
Problem Statement
Compute the value of the sum
\begin{align*}
\frac{1}{1 + \tan^3 0^\circ}
&+ \frac{1}{1 + \tan^3 10^\circ} + \frac{1}{1 + \tan^3 20^\circ}
+ \frac{1}{1 + \tan^3 30^\circ} + \frac{1}{1 + \tan^3 40^\circ} \\
&+ \frac{1}{1 + \tan^3 50^\circ} + \frac{1}{1 + \tan^3 60^\circ}
+ \frac{1}{1 + \tan^3 70^\circ} + \frac{1}{1 + \tan^3 80^\circ}
\, .
\end{align*}