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The Nottingham champion and Eastbourne quarter-finalist was then broken twice more to leave Martic only needing to win her next three service games.
BBC: Elena Baltacha, Melanie South & Katie O'Brien go out
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"I'm dead excited as it's my first time there, " said the man who has been a UK Championship (1999) and LG Cup (2003) quarter-finalist.
BBC: SPORT | Other Sport | Snooker | Holt gears up for Hunter reunion
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Watson, a quarter-finalist in this year's Australian Open juniors, held the opening game of the second set and broke again to go 2-0 up.
BBC: Watson wins US Open girls' title
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Liang, the 2008 world quarter-finalist, who recently earned a place in the provisional top 16 rankings, kept battling and won three in a row which included knocks of 61 and a 103.
BBC: Ronnie O'Sullivan through despite wobble against Liang
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Earlier Federer survived a loss of form in a scrappy second set before finally coming through in four sets against Robredo, world number 52 and a quarter-finalist in this tournament four years ago.
BBC: Roger Federer & Novak Djokovic progress at Aussie Open
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Singapore may field three badminton players at the Commonwealth Games who have come from Indonesia, and Hong Kong could have one, in addition to their former world women's singles quarter-finalist Wang Chen, who crossed the border from China to the former British colony.
BBC: Defecting dilemmas for Games
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Earlier, Jamea Jackson stunned last year's beaten finalist and eighth seed Jelena Jankovic to book her place in the quarter-finals.
BBC: SPORT | Tennis | Sharapova wins as form improves