The equation whose roots are tan^2 π/7, tan^2 3π/7 and tan^2 5π/7 is

Let x^3 + bx^2 + cx+d = 0 be the equation

b = -(tan^2 π/7 + tan^2 3π/7 + tan^2 5π/7) ;

c= ( 2*tan^2 π/7 * tan^2 3π/7 + 2 *tan^2 3π/7 *tan^2 5π/7 + 2 *tan^2 2π/7 *tan^2 5π/7) ;

d = – (tan^2 π/7* tan^2 3π/7 * tan^2 5π/7);

using trigonometric identity you can simplify