parametric integral and asymptotic representation

Question

Here is a parametrial integral $$I(a)=\int_0^{\pi}\int_0^{\pi} \frac{1-a\big(1-\frac{{\cos}x+{\cos}y}{2}\big)}{\sqrt{-{\cos}^2(x/2){\cos}^2(y/2)+\big[1-a\big(1-\frac{{\cos}x+{\cos}y}{2}\big)\big]}}dxdy$$ with $0<a<1$.After some trials It can be rewriten as $$I(a)=\int_0^{1}\int_0^{1}\frac{1-a(u+v)}{\sqrt{\big[1-a(u+v)\big]^2-(1-u)(1-v)}\sqrt{u(1-u)}\sqrt{v(1-v)}} dudv$$ However, I cannot go any further though I notice the fact that the integrand, defined as $f(x,y)$, satisfies the symmetry relation $$f(x,y)=f(y,x)$$. I don't know whether there exit a closed form of the integral $I(a)$or not. If not, can we find the asymptotic representation of the integral around $a=\frac12$, saying $a\rightarrow \frac12^{-}$ and $a\rightarrow \frac12^{+}$, respectively.