Question: simplify sin/cos with multiples of Pi

In the following examples I attempt to remove integer multiples of Pi from sin/cos. Nothing works.

Why? How do I make it work?

Thank you.

term1:=cos(Pi*(3*a-2*n));
> term2:=cos(3*Pi*a+2*Pi*n);
> term3:=cos(3*Pi*a-2*Pi*n);

                     term1 := cos(Pi (3 a - 2 n))


                    term2 := cos(3 Pi a + 2 Pi n)


                    term3 := cos(-3 Pi a + 2 Pi n)

> combine(term1) assuming n,posint;
> simplify(term1) assuming n,posint;

                         cos(3 Pi a - 2 Pi n)


                         cos(Pi (3 a - 2 n))

> combine(term2) assuming n,posint;
> simplify(term2) assuming n,posint;

                         cos(3 Pi a + 2 Pi n)


                         cos(3 Pi a + 2 Pi n)

> combine(term3) assuming n,posint;
> simplify(term3) assuming n,posint;

                         cos(3 Pi a - 2 Pi n)


                         cos(3 Pi a - 2 Pi n)

> combine(term1+term2) assuming n,posint;
> combine(term1+term3) assuming n,posint;

             cos(3 Pi a - 2 Pi n) + cos(3 Pi a + 2 Pi n)


                        2 cos(3 Pi a - 2 Pi n)

>