Don't just try to simplify immediately. First, find more relationships. Note that you can reduce any term of for to an expression where the highest power of is 2.

Also note that if you do this for , the expression you get is exactly the one you would get from . So, these expressions become exhaustive fairly quickly.

Next, remember that you are using the rationals, so you need to figure out inverse powers of theta, too.

so

Again, these expressions become exhaustive fairly quickly.

Does that help at all?