Solve for S_1
S_{1}=\frac{2\sqrt{7}\left(2\pi -1\right)\left(\arctan(\frac{5\sqrt{7}}{7})-\arctan(\frac{\sqrt{7}}{7})\right)}{7}\approx 2.886392945
Assign S_1
S_{1}≔\frac{2\sqrt{7}\left(2\pi -1\right)\left(\arctan(\frac{5\sqrt{7}}{7})-\arctan(\frac{\sqrt{7}}{7})\right)}{7}
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