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- f[[Theta]_] =
- Integrate[1/(Cot[[Theta]]^2 - Sin[[Theta]]^2)^((1/2)), [Theta]]
- -(1/Sqrt[Cot[[Theta]]^2 - Sin[[Theta]]^2])
- 2 (-9 + 4 Sqrt[5]) Cos[[Theta]/2]^4 Csc[[Theta]] EllipticF[
- ArcSin[Sqrt[9 + 4 Sqrt[5]] Tan[[Theta]/2]^2],
- 1/(9 + 4 Sqrt[5])^2] Sqrt[9 + 4 Sqrt[5] - Tan[[Theta]/2]^4] Sqrt[
- 1 - (9 + 4 Sqrt[5]) Tan[[Theta]/2]^4]
- InverseFunction[f][1]
- [Theta]1[t_] := NSolve[f[[Theta]] == t, {[Theta]}]
- [Theta]1[1]
- f[θ_] = Integrate[1/Sqrt[Cot[θ]^2-Sin[θ]^2], θ];
- Plot[-(1/Sqrt[Cot[θ]^2-Sin[θ]^2])f[θ] ,{θ,-4 π, 4 π},PlotRange->{0,2}]
- FindRoot[-(1/Sqrt[Cot[θ]^2-Sin[θ]^2])f[θ]==1 ,{θ,5.5}]
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