MathDB

There are 6 distinct values of

x

strictly between

0

and

\frac{\pi}{2}

that satisfy the equation

\tan(15 x) = 15 \tan(x) .

Call these 6 values

r_1

r_2

r_3

r_4

r_5

, and

r_6

. What is the value of the sum

\frac{1}{\tan^2 r_1} + \frac{1}{\tan^2 r_2} + \frac{1}{\tan^2 r_3} + \frac{1}{\tan^2 r_4} + \frac{1}{\tan^2 r_5} + \frac{1}{\tan^2 r_6} \, ?

20