inequality

do you need A,B,C to be acute angles of a triangle?

ASSUMING ANGLES ARE ACUTE
consider the graph of secx in x →(0,π/2)
now
consider points x_1 ,x_2 ,x_3
such that
x_1 + x_2 +x_3 = π
now a triangle will be formed using
f(x_1),f(x_2)and f(x_3)
the y-cordinate centroid of this triangle will be always lying above f(x_1 +x_2 +x_3 /3) i.e
f(x- cordinate of centroid)
hence we get the inequality
secA+secB+secC /3 ≥ sec(pi/3)
secA+secB+secC ≥6