You transcribed the formula incorrectly. The term is -(alpha / 24). You calculated -1 / (24 · alpha). The correct derivation is: 1 / alpha = S - (alpha / 2

You transcribed the formula incorrectly. The term is -(alpha / 24). You calculated -1 / (24 · alpha). The correct derivation is: 1 / alpha = S - (alpha / 24) 1 = S · alpha - (alpha^2) / 24 alpha^2 - 24 · S · alpha + 24 = 0 Solving this with S = 4 · π^3 + π^2 + π yields the correct value.