I figured out that θ is 30 degrees. After simplifying I still could not eliminate the xy-term: I ended up with:
10x2 - 6xy + 10y2 + 3(sqrt(3))x2 - 3(sqrt(3))y2 -32 = 0
note: the x and y terms above are in prime form (I just don't know how to show that on a forum)
As you can see I still have a...