I added a slight variation "Musíme ta okna otevřít něčím." which sounds better to me, although the stress at "něčím" in the final position is unusual. Maybe someone will add more comments to your word order and perhaps we will add it later.
My answer -- Něčím musíme otevřít ta okna -- was considered incorrect, but I will report it in case it's an acceptable, but missing, translation. If it's totally wrong, would someone please tell me why?