Can Maple determine the value of DthetaZero such that the solution to the ODE, for some specific value of t, simultaneously provides the two values theta(t)=Pi and diff(theta(t),t)=0?
sol:=dsolve({4*sin(theta(t))*cos(theta(t))-9.8100*sin(theta(t))-(diff(theta(t), t, t)) = 0, theta(0) = 2*Pi*(1/3), D(theta)(0) = DthetaZero}, numeric)
odeplot(sol,[t,theta(t),diff(theta(t),t)],t=0..5) for trial values of DthetaZero shows that the desired value is
1.0340*Pi <DthetaZero<1.0345*Pi.