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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