We sketch our solution region.

Input := 


cAnswer = ParametricPlot[{Cos[t],Sin[t]},

				{t,0,2Pi - thetaOfCut},

			Axes->False, AspectRatio->Automatic]

Output =


-Graphics-

Input := 


l1Answer = Graphics[Line[{{0,0}, {Cos[0], Sin[0]}}]]

Output =


-Graphics-

Input := 


l2Answer = Graphics[Line[{{0,0}, 

		{Cos[2 Pi - thetaOfCut], Sin[2 Pi - thetaOfCut]}}]]

Output =


-Graphics-

Input := 


Show[cAnswer,l1Answer,l2Answer,Axes->True]

Output =


-Graphics-