Who ever put this lesson together does not understand English. So frustrating.. cannot get through this lesson. In English "even in summer" is correct. English does not require the definite article. Tough tough lesson. :(
I don't think in English you need to put the definite article before summer. In fact it even sounds a bit awkward, don't you think? You would need the definite article "the" only if you were referring to a specific summer, not summer in general.