If ∫_0^((π)/4) (sin^2 x)/(1+ sin x cos x) d x=1/a log_e (a/3)+(π)/(b √ 3), where a, b ∈ N, then a + b is equal to ____.

If $\displaystyle \int_0^{\frac{\pi}{4}} \frac{\sin ^2 x}{1+\sin x \cos x} \mathrm{~d} x=\frac{1}{\mathrm{a}} \log _{\mathrm{e}}\left(\frac{\mathrm{a}}{3}\right)+\frac{\pi}{\mathrm{b} \sqrt{3}}$, where $\displaystyle \mathrm{a}, \mathrm{b} \in \mathbf{N}$, then $\displaystyle \mathrm{a}+\mathrm{b}$ is equal to $\displaystyle \_\_\_\_$.