Evaluate limit as x approaches pi of 4sin(x+sin(x))

Take the limit of each term.
Move the term outside of the limit because it is constant with respect to .
Move the limit inside the trig function because sine is continuous.
Split the limit using the Sum of Limits Rule on the limit as approaches .
Move the limit inside the trig function because sine is continuous.
Evaluate the limits by plugging in for all occurrences of .
Evaluate the limit of by plugging in for .
Evaluate the limit of by plugging in for .
Simplify each term.
Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.
The exact value of is .