"This year is the beginning of a long and difficult war.”
“This year” is the subject, “(is) the beginning” is the predicate. You may not have covered this yet, but in Greek predicates normally go without the article. So you’d do better to cancel ἡ.
I should think that the rule is more like ‘in Greek (definite nominal) predicates that precede the verb go without the article’. If the predicate were after the verb we would expect an article (all other factors unconsidered). No?
[*] 1150. A predicate noun has no article, and is thus distinguished from the subject: καλεῖται ἡ ἀκρόπολις ἔτι ὑπ᾽ Ἀθηναίων πόλις the acropolis is still called ‘city’ by the Athenians T. 2.15.
Yes that’s it. Remember the verb to be can’t have an object, only what grammarians call a predicate (whether noun or adjective).
“X is Y”, “X is called Y”, “X seems to be Y”, “X can’t become Y". In all such cases Y will be nominative, in agreement with X.
Predicates can be in other cases too, for X is not always nominative. “She wanted the white roses to be red.” “She painted the white roses red.” “red” will be accusative, agreeing with “the white roses”, the object.
It’s “predicative” as distinct from “attributive” (“She painted the white roses”).
[@Callisper. I don’t know what’s gained by “definite nominal” (if it were indefinite of course it wouldn’t have the article, and it doesn’t apply only to nouns). And I don’t think its position relative to the verb is determinative; you may know more about that than I do. For present purposes I thought it enough to say “normally"; bedwere’s Smyth quote is far from absolute, but I see no reason to use the article here.]