A calculus problem by Jose Sacramento

$\large \int_0^\pi \ln \left( \dfrac{3- \cos x}{2 - \cos x} \right) \, dx$ If the integral above can be expressed as $\pi \ln \left( \dfrac{ a + \sqrt{b-1}}{c + \sqrt{d-1}} \right)$ , where $a,b,c,d$ are all integers, find the sum $a+b+c+d$ .