Differential Equations: JEE Main 2022 Mathematics question

Let $S = (0,2\pi ) - \left\{ {{\pi \over 2},{{3\pi } \over 4},{{3\pi } \over 2},{{7\pi } \over 4}} \right\}$. Let $y = y(x)$, x $\in$ S, be the solution curve of the differential equation ${{dy} \over {dx}} = {1 \over {1 + \sin 2x}},\,y\left( {{\pi \over 4}} \right) = {1 \over 2}$. If the sum of abscissas of all the points of intersection of the curve y = y(x) with the curve $y = \sqrt 2 \sin x$ is ${{k\pi } \over {12}}$, then k is equal to _____________.