RU-ALLRUSSIAN 1988 Problem 10

A, B, C are the angles of a triangle. Show that $2(\sin \mathrm{A}) / \mathrm{A} + 2(\sin \mathrm{B}) / \mathrm{B} + 2(\sin \mathrm{C}) / \mathrm{C} \leq (1 / \mathrm{B} + 1 / \mathrm{C}) \sin \mathrm{A} + (1 / \mathrm{C} + 1 / \mathrm{A}) \sin \mathrm{B} + (1 / \mathrm{A} + 1 / \mathrm{B}) \sin \mathrm{C}$ .