Can somebody clarify me how to estimate number of iterations required for a particular accuracy in bisection method ?

i.e

think we want to know a real solution of x+sin(x)=pi/2 between pi/2 n 2pi

How many iterations do we need to get x with an accuracy of 3 decimal places using bisection method ? (without doing any iterations)

please tell me if you don`t get the idea of my Qn .

Thank You