If \(\int_0^{\frac{\pi}{4}} \frac{\sin ^2 x}{1+\sin x \cos x} d x=\frac{1}{a} \log _e\left(\frac{a}{3}\right)+\frac{\pi}{b \sqrt{3}}\), where a, b ∈ N, then a + b is equal to ______
Enter numerical value using the virtual keypad. Round off where necessary.