Let $L = \{wcw : w \in \{a, b\}^\ast\} \subseteq \{a, b, c\}^\ast$. From what I know, this language is not a context-free language but how about complement of this language?

I know that the class of CFLs is not closed under complement, so there is no easy way to decide (this problem is undecidable in general) but I don't know whether in this particular example the complement is a CFL, I only know that this language is decidable.