csc(75)=1/sin(75)
sin(a+b)=sin(a)cos(b)+sin(b)cos(a)
sin(75)=sin(45+30)=sin(45)cos(30)+sin(30)cos(45)
using a 30-60-90 triangle you can evaluate this expression and you get the answer:
(sqrt(6)+sqrt(2))/4. and since csc is 1/sin, the answer to csc(75)=4/(sqrt(6)+sqrt(2))
approx=1.035277