Iteration A level maths question help!!!

I’ve been struggling with this question..
Ive attached it below
I know i need to do 3=3 in my calculator and then put Ans whenever there is an x.. but i have no idea if im putting the Ans in the wrong places because im not getting close to the answer?!
This is what i put in my cal (where Ans=3)
-sin(4Ans)+e^(-Ans)+0.75/4cos(4Ans)-e^(-Ans)
And what is the Xn before it? Is that why im getting it wrong? But idk what Xn actually is so not sure.

I’ve been struggling with this question..
Ive attached it below
I know i need to do 3=3 in my calculator and then put Ans whenever there is an x.. but i have no idea if im putting the Ans in the wrong places because im not getting close to the answer?!
This is what i put in my cal (where Ans=3)
-sin(4Ans)+e^(-Ans)+0.75/4cos(4Ans)-e^(-Ans)
And what is the Xn before it? Is that why im getting it wrong? But idk what Xn actually is so not sure.

Im presuming youve got a description of newton-raphson so something like page 75 in
https://www.lboro.ac.uk/media/media/schoolanddepartments/mlsc/downloads/HELM%20Workbook%2031%20Numerical%20Methods%20of%20Approximation.pdf
The key idea of iteration is that you use an old value to calculate a new value so something line
new value = old value - f(old value)/f'(old value)
then set
old value = new value
and repeat.
Here the initial old value = 3 so you calculate
new value = 3 - f(3)/f'(3)
so the new value is now 2.92 and then set
old value = 2.92
and keep repeating.
The key idea is that you guess value of the root. Then evaluate both the functions and the derivative value at that guess so you form the tangent line at your guess and if that is a good approximation of the function close to the root, then you can use where the tangent line crosses the x-axis (new root estimate) to improve it. The iterative scheme will converge when the estimate does not change.

I think i understand this but what do i put in my calculator? As i think i am missing something when i put it in as i said above??