Trigonometry, eliminate theta

Solution 1:

HINT:

  1. Notice that $x+y=2\sin\theta$ and $x-y=2\tan\theta$.
  2. Recall that $\tan\theta\equiv\frac{\sin\theta}{\cos\theta}$
  3. Recall that $\sin^2\theta + \cos^2\theta \equiv 1$
  4. Consider $(x+y)^2$ and $(x-y)^2$ in terms of $\theta$