Here's the sentence :
さてと・・・それじゃあ捜査を始めるとしようか。
I would have understood if the sentence was : "さてと・・・それじゃあ捜査を始めよう", but I don't understand the rest of the sentence. Is "としよう" some kind of grammar ?
As for the context, the characters were just about to investigate a murder.