Words which, cyclically shifted twice, equal their reverse
Let us see which words satisfy $C_2(w) = w^R$. Write $w = \sigma \tau x$, where $\sigma,\tau \in \Sigma$ and $x \in \Sigma^*$. Then $C_2(w) = x \sigma \tau$ and $w^R = x^R \tau \sigma$, and so $C_2(w) = w^R$ iff $x = x^R$ and $\sigma = \tau$.
You should be able to use this information in order to construct a grammar for your language.