= Solution
Every term in the free energy contracts the vector components with the <inner product>[Euclidean inner product]: it depends only on $|\mathbf p|^2$, $|\mathbf p|^4$, $(\nabla_i p_j)(\nabla_i p_j)$, and $|\nabla^2\mathbf p|^2$. A constant $\mathcal R\in SO(3)$ preserves all these contractions and commutes with spatial differentiation. Therefore
$$
F[\mathcal R\mathbf p]=F[\mathbf p],
$$
so every constant rotation of candidate (ii) has the same free energy. The orientation of the rotation plane of the <polar helical smectic> is thus continuously degenerate.
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