Ellipse question

So cos(θ) = -0.5 (meaning θ = 120 or 240 degrees) and sin(θ) = 0 (meaning θ = 0 or 180 degrees). How do I determine which θ value is the correct one (question says value rather than values). Also, the last line doesn't make any sense?

P = (3cos(θ), 2sin(θ)) so surely if you plug in cos(θ) = -0.5
and sin(θ) = 0 you get P = (-3/2, 0) ?

Is this a mark scheme you've quoted or something out of a book?

I haven't time to look in detail now, but it certainly looks like there is more than one possibility for theta!

Its out of a book. The questions says value so there can only be one value for theta in this case (unless the question is wrong?).