Solution
= Solution
The polynomial $X^3+2X^2+1$ is irreducible by the rational-root test. The power basis $1,\theta,\theta^2$ has discriminant
$$
\operatorname{disc}(X^3+2X^2+1)=-59.
$$
For the order $\mathbb Z[\theta]\subseteq\mathcal O_L$,
$$
\operatorname{disc}(\mathbb Z[\theta])
=[\mathcal O_L:\mathbb Z[\theta]]^2d_L.
$$
Since $59$ is squarefree, the index can only be one. Hence
$$
\boxed{\mathcal O_L=\mathbb Z[\theta]}.
$$