Chapter 8.1, Problem 7E

In Problems 1-8, determine the first three nonzero terms in the Taylor polynomial approximations for the given initial value problem.

$y^{″}\left(\theta \right)+y{\left(\theta \right)}^3=\sin \theta$;

$y\left(0\right)=0$, $y^{\prime }\left(0\right)=0$