Any way you slice it

Geometry Level 5

Suppose that two distinct lines passing through the origin cut through the region RR in the first quadrant bounded by the xx-axis and the circle (x1)2+y2=1(x - 1)^{2} + y^{2} = 1 such that the lines divide RR into 33 subregions of equal area.

If the sum of the slopes of these two lines is SS, find 1000S\lceil 1000*S \rceil.

Note: Numerical methods can be used in the process of solving this question.

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