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Finding branches where general solution is possible


For following function with period 2 Pi in which branches is it possible to get a general solution?

Regards
Narasimham 

DSolve[{si''[th] Tan[si[th]]==(1+si'[th]) (1+2si'[th]),si[0]==Pi/4 },si,th]
NDSolve[{si''[th] Tan[si[th]]==(1+si'[th]) (1+2si'[th]),si'[0]==0,si[0]==Pi/4},si,{th,0,6Pi}];
SI[u_]=si[u]/.First[%];Plot[SI[th],{th,0,6Pi}]

DSolve::bvnul: For some branches of the general solution, the given boundary conditions lead to an empty solution.>>



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