Can you use this combo to do 3 points of extra ranged damage?

Yes.

For future reference it's always worth quoting the text from relevant cards when asking these sorts of questions. I just had to spend 30 seconds looking for the battle rage card text(as it's not one that I've come across often in gameplay and am therefore unfamiliar with it). I appreciate that's not a lot of time, but I'm sure plenty of people will just pass on a question they would be able to answer quite easily if the relevant information was there for them.

For anyone else wondering: "battle rage" is a yellow neutral 1 cost event which states "Spot a Character that has 6 or more damage on it. Resolve one of that characters character dice showing damage, increasing its value by 2.

Aurra Sing: Before you resolve this die you may discard a card from your hand to increase it's value by 1.

Ok, thanks, will do in the future.

I like to go to swdestinydb search for the card and then right click on the image and select "Copy Image Location" .

Then just paste this into my post, which then inserts the scanned image of the card.

I like this as there is no chance of typing in the text with an error and you get the image of the card which help people recognise it. Most people don't read cards when their opponent plays them but identifies the cards from the images.

Stu35 is correct in his ruling, you are resolving a card in playing the Battle Rage, as Aura's ability has the Before keyword you can trigger that ability at any time one of her dice is resolved, perhaps your opponent played doubt so it will trigger even when it isn't your turn or action.