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4/(-1 + Cot[x/4])

Integrate[1/(1 - Sin[x/2]), x] ==
4/(-1 + Cot[x/4]) 

              1
Integrate[----------, x] == 
                  x
          1 - Sin[-]
                  2

     4
-----------
         x
-1 + Cot[-]
         4
Time to compute: 0.03 second
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