Cutting across a Trig

Level pending

Consider the intersection points of the curve \[y=2 \sin \frac{\pi}{8}x \quad (x \geq 0)\] and the line \(y=1\). If \(x_1\), \(x_2\), \(x_3\), \(\cdots\) are the \(x\)-coordinates of those points in ascending order, what is the value of \[x_1+x_2+x_3+x_4+x_5+x_6?\]

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