せっかく
specially, (it's a shame to waste) the effort or chance
せっかく + Verb … のに / から · せっかくの + Noun
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せっかく marks something as valuable because of the effort, trouble or rarity behind it, and says it would be a shame to waste it.
With のに, the effort was wasted: せっかく作ったのに、誰も食べてくれなかった, "I went to the trouble of making it, and nobody ate it".
With から or なら, it's a reason to make the most of it: せっかく京都に来たんだから、お寺を見に行こう, "since we've come all the way to Kyoto, let's see a temple".
With の and a noun, it's a precious thing: せっかくの休み, "my precious day off".
せっかくですが is the polite way to turn down an offer: "it's very kind of you, but…".
Examples
せっかく作ったのに、誰も食べてくれなかった。
I went to the trouble of making it, but nobody ate it.
せっかく京都に来たんだから、お寺を見に行こう。
Since we've come all the way to Kyoto, let's go and see a temple.
せっかくの休みなのに、雨だ。
It's my precious day off, and it's raining.
せっかくですが、今回は遠慮します。
It's very kind of you, but I'll pass this time.
せっかくのチャンスだから、やってみたら?
It's a rare chance, so why not give it a try?