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3 XX - best line?

In a club session, you have the following auction, where partner opens a strong, forcing 2 and shows a balanced hand with 20-21 hcp. Then the auction becomes a little more unusual...

North
AJ6
AK2
KJ7
A643
South
8752
J105
A864
85
W
N
E
S
P
2
P
2
P
2NT
P
3
X
3
X
XX
P
P
P

We have no agreement about the difference between bidding 3 instead of passing the lead directional double; partner just ignores the double. LHO doubles 3, presumably natural, showing diamonds. Figuring that we have a poor club holding (and feeling a bit frisky) we redouble, hoping for partner to have a four card diamond suit since he denied a major and LHO made a lead directional double of clubs. Partner passes. 

Feel free to critique our bidding or our lack of agreements about defense against lead directional doubles. The main question in this article, however, is how to play 3 XX at matchpoints. LHO leads 2.

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