どうせ
anyway (resigned), in any case
どうせ + Sentence · どうせ〜なら
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どうせ says the outcome is fixed whatever you do, usually with resignation or cynicism: どうせ間に合わないから、ゆっくり行こう, "we won't make it anyway, so let's take our time".
About yourself, it can be self-pitying: どうせ私には無理だよ, "it's no use, I can't do it anyway".
With なら, it's more positive: "if it's going to happen anyway, let's make the most of it": どうせやるなら、楽しくやろう, "if we're doing it anyway, let's have fun".
Compare せっかく, which values effort and doesn't want to waste it. どうせ has given up on changing the result.
Examples
どうせ間に合わないから、ゆっくり行こう。
We won't make it anyway, so let's take our time.
どうせ私には無理だよ。
It's no use, I can't do it anyway.
どうせ買うなら、いい物を買いたい。
If I'm going to buy one anyway, I want a good one.
どうせ誰も見ていないんだから。
Nobody's watching anyway.
どうせやるなら、楽しくやろう。
If we're doing it anyway, let's have fun with it.