The positive roots of the equation x + TaNx = 0 are arranged as A1, A2, A3,..., an from small to large 1 0

Make the line Y1 = - X and tangent curve y2 = TaNx respectively
Then the intersection of them is the root of X + TaNx = 0
Then in every period π, there is an intersection point between Y1 and Y2,
If x > 0 is the positive root, the intersection points are all in the half period that makes TaNx negative, so there is: π / 2A (n + 2) + an, that is 4-to-3

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