PI in ].0,4.[ by SIN_COS:def 28;
then A1: PI > 0 by XXREAL_1:4;
then A2: (3 / 4) * PI < PI by XREAL_1:157;
(3 / 4) * PI > (3 / 4) * 0 by A1, XREAL_1:68;
hence (3 / 4) * PI in ].0,PI.[ by A2, XXREAL_1:4; :: thesis: verum