MLE of SDE linear in parameter

Question

I am given an example SDE: $$dX_t=\langle \theta, f_t(X)\rangle dt + \varepsilon dW_t, X_0=x_0, 0\leq t\leq T$$ and $f_t$ is a function that satsfies most conditions we could need. The book then states that the maximum likelihood estimator is $$\hat\theta_\varepsilon = I_T^{-1} \int_0^Tf_t(X) dX_t$$ where $$I_T=\int_0^T f_t(X)f_t(X)^\dagger dt$$, $\dagger$ being the transpose. I am having troubles understanding where this comes from. I think it should be straightforward once I know what the likelihood function of X is, but since it was introduced as the Radon-Nikodym density, I don't see a way how one could caluclate it directly. I am just getting used to the topic, so I think I am only missing something minor here. For reference, I am looking at the book "Identification of Dynamical Systems with Small Noise" by Kutoyants, the example comes after equation (1.60).