Another approach is to note

1) (x/2)^2 +(y/3)^2 = 1 using x/2 = cos(a) y/3 = sin(a)

and y = 2/3 x + 5sqrt(2)/6

substitute this into 1)

Still it won't be pretty and I hope you have a computer or calculator to

solve.

See attachment where I have used Mathcad to solve the problem