If K=𝐐(θ) where θ∈𝐑 and θ^1=3, verify Corollary 8.3 for the additive subgroup of K generated by

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Step 1: Identify the field u005C( K u003D u005Cmathbf{Q}(u005Ctheta) u005C) where u005C(u005Cthetau005C) is a real number such t

If $K=\mathbf{Q}(\theta)$ where $\theta \in \mathbf{R}$ and $\theta^1=3$, verify Corollary 8.3 for the additive subgroup of $K$ generated by $1+\theta$ and $\theta^2-2$.