What does it mean? "Trying to be asked for answers, I can't say anything" looks strange...
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Even if [you] demand an explanation, [I] can not say anything.
volitional-form + が/と is a literary way of saying "even if ～" or "regardless of ～". Usually (but not always) there is a comma after the が/と.
Examples on JGram:
volitional-form + と can be actual volition followed by a quotative particle, depending on what follows:
I think I will demand an explanation.
There is a great page :
Meaning: even if one tries to do something, it can’t be done
I tried to call Jake, but my voice was gone.
[ 呼ぼうにも] -- This part feels like the subjunctive of European languages.
Were I to call Jake ...
Even if I were to call Jake ...
Even if I would want to call Jake ...
Even if I would've wanted to call Jake ... Try as I might to call Jake ...
When the [1st person] is trying, it's ～しようにも
When the [Another party] is trying/asking, it's ～しようと, ～しようとも, etc. (See Choco-san's link).
e.g. -- どんなに激しく雨が降ろうと、この家の屋根は大丈夫だ。