[math-fun] another circuitous derivation

had among its terminal nodes In[652]:= Sum[(-1)^n*ArcTan[Csch[Pi*(n - 1/2)/Sqrt[3]]], {n, \[Infinity]}] == -5*Pi/24 Out[652]= 1 (n - -) Pi n 2 Sum[(-1) ArcTan[Csch[-------------]], n >= 1] Sqrt[3] 5 Pi = - ----. 24 It doesn't *look* that hard ... Joerg? Easy warmup: In[654]:= Product[Coth[Pi*(n-1/2)]^8, {n, \[Infinity]}] == 2 Out[654]= 1 8 Product[Coth[(n - -) Pi] , n >= 1] = 2. 2 --rwg