If and , then find the value of .

If $\cos^{-1}\frac{x}{a} - \cos^{-1}\frac{y}{b} = \frac{\pi}{3}$ and $\sin^{-1}\frac{x}{a} + \sin^{-1}\frac{y}{b} = \frac{2\pi}{3}$, then find the value of $4\frac{x^2}{a^2} + \frac{y^2}{b^2}$.