In questions of example 5 why do we split the numbers in terms of pi/4 and pi/6 though when added they don't give the original value?

Dear Student, 
In the question 5, the solution has to be solved as given.
We need to split because we know the direct values of pi/4 or pi/6.
Obviously, when we put the values we get simplified answer or exact value of givev function.

Hope it clears your doubt.
Regards!