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Let S=(0,2pi)-{(pi)/(2),(3pi)/(4),(3pi)/...

Let `S=(0,2pi)-{(pi)/(2),(3pi)/(4),(3pi)/(2),(7pi)/(4)}`. Let `y=y(x),x in S` be the solution curve of the differential equation `(dy)/(dx)=(1)/(1+sin2x),y((pi)/(4))=(1)/(2)`. If the sum of abscissas of all the points of intersection of the curve `y=y(x)` with the curve `y=sqrt(2)sinx` is `(kpi)/(12)`, then k is equal to ________

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