an adverb meaning 'in any case' or 'anyhow' — used to state that the result is the same regardless.
どのみち彼はその提案を断るだろう。
In any case, he'll probably reject that proposal.
時間がない。どのみち今日は無理だ。
There's no time. In any case, today is impossible.
どのみち結果は同じだから、細かいことは気にしないでいい。
The result will be the same anyway, so don't worry about the small details.