ILL 1986 Problem 78

If $T$ and $T_1$ are two triangles with angles $x, y, z$ and $x_1, y_1, z_1$ , respectively, prove the inequality $$\frac{\cos x_1}{\sin x}+\frac{\cos y_1}{\sin y}+\frac{\cos z_1}{\sin z} \leq \cot x+\cot y+\cot z.$$