Show that for three real number that satisfy 0 < x < y < z < π/2 , the following inequality holds: (x+y) sin(z) + (x-z) sin(y) < (y+z) sin(x)

Inequality.py

import math
import random

count = 0
n = 1000000         #montecarlo simulation
for i in range (1000000):
   z = float(random.uniform(0,(math.pi)/2))     #uniform distribution, it gives a random real number between (0, π/2)
   y = float(random.uniform(0,z))
   x = float(random.uniform(0,y))
   side_1 = float((x+y) * math.sin(z) + (x-z) * math.sin(y))
   side_2 = float((y+z) * math.sin(x))


   if side_1 < side_2 :           # inequality we want to prove
      count = count + 1           # every time the inequality has proved, we add 1 to the variable "count"


print('The inequality has been true:', count, 'times')
print()

if count == n:         # condition in order to prove the inequality
    print (' "n" and "count" are equal so the inequality is almost certainly true')