IMO 1966 LL USS5

Prove the inequality

IMO 1966 LL USS5

Origin: USS

Problem

Prove the inequality tan \pi sin x 4 sin \alpha + tan \pi cos x 4 cos \alpha > 1 for any x, \alpha with 0 \leqx \leq\pi/2 and \pi/6 < y < \pi/3.