Question: When did the head coach who led the Razorbacks to victory in the 1960 Gator Bowl retire?

Context paragraphs:
1960 Arkansas Razorbacks football team: The 1960 Arkansas Razorbacks football team represented the University of Arkansas in the Southwest Conference (SWC) during the 1960 college football season.  In their third year under head coach Frank Broyles, the Razorbacks compiled an 8–3 record (6–1 against SWC opponents), won the SWC championship, and outscored all opponents by a combined total of 185 to 87.  The Razorbacks' only losses during the regular season came against Baylor by a 28–14 score and to Mississippi by a 10–7 score.  The team was ranked #7 in both the final AP Poll and the final UPI Coaches Poll and went on to lose to Duke in the 1960 Cotton Bowl Classic by a 23–14 score.

1960 Gator Bowl (December): The 1960 Gator Bowl was a post-season college football bowl game between the Baylor Bears of the Southwest Conference (SWC) and the Florida Gators representing the Southeastern Conference (SEC).  Florida defeated Baylor 13–12.  Both quarterbacks were the game's Most Valuable Player: Florida's Larry Libertore and Baylor's Bobby Ply.

1959 Arkansas Razorbacks football team: The 1959 Arkansas Razorbacks football team represented the University of Arkansas in the Southwest Conference (SWC) during the 1959 college football season.  In their second year under head coach Frank Broyles, the Razorbacks compiled a 9–2 record (5–1 against SWC opponents), finished in a tie with Texas for the SWC championship, and outscored all opponents by a combined total of 163 to 101.  The Razorbacks' only losses came against Texas by a 13–12 score and to Mississippi by a 28–0 score.  The team was ranked #9 in both the final AP Poll and the final UPI Coaches Poll and went on to defeat Georgia Tech in the 1960 Gator Bowl by a 14–7 score.  Halfback Jim Mooty was selected by the Associated Press as a first-team player on the 1959 All-America Team.

Frank Broyles: John Franklin Broyles (December 26, 1924 – August 14, 2017) was an American football player and coach, athletics administrator, and broadcaster.  He served as the head football coach at the University of Missouri in 1957 and at the University of Arkansas from 1958 to 1976.  Broyles also was Arkansas' athletic director from 1974 until his retirement on December 31, 2007.

2011 Florida Gators football team: The 2011 Florida Gators football team represented the University of Florida in the sport of American football during the 2011 college football season.  The Gators competed in the Football Bowl Subdivision (FBS) of the National Collegiate Athletic Association (NCAA) and the Eastern Division of the Southeastern Conference (SEC).  They played their home games at Ben Hill Griffin Stadium on the university's Gainesville, Florida campus, and were led by first-year head coach Will Muschamp.  Muschamp coached the Gators to a third-place finish in the SEC East, a 3–5 conference record, a 24–17 Gator Bowl victory over the Ohio State Buckeyes, and an overall win-loss record of 7–6 (.539).

2010 Michigan Wolverines football team: The 2010 Michigan Wolverines football team represented the University of Michigan in the 2010 NCAA Division I FBS football season.  Michigan played its home games at Michigan Stadium in Ann Arbor, Michigan and competed in the Big Ten Conference.  The season was the first since the renovation of Michigan Stadium, begun in 2007, was completed.  The Wolverines were led by third-year head coach Rich Rodriguez.  After its week 10 win against Illinois, Michigan became bowl eligible for the first time since 2007, and later accepted a bid to play in the Gator Bowl against Mississippi State on January 1, 2011, losing 52–14.  The Wolverines finished the season sixth out of 120 Division I FBS teams in total offense, 110th in total defense and 112th in passing defense.  Michigan finished with an overall record of 7–6, 3–5 in Big Ten play.  After the season, head coach Rich Rodriguez and his staff were dismissed on January 5, 2011.

2011 Gator Bowl: The 2011 Gator Bowl game was a post-season college football bowl game between the Michigan Wolverines of the Big Ten and Mississippi State Bulldogs of the SEC, and was played on January 1, 2011 (1:30 p.m. ET), at EverBank Field in Jacksonville, Florida.  It was the 66th edition of the bowl game and was broadcast by ESPN2.  It was the first time these two teams have ever met.  After the game started fairly close, Mississippi State ultimately pulled away and routed Michigan 52-14.  It was the most points ever scored by one team in the Gator Bowl, and the worst loss Michigan has ever suffered in any bowl game in its long history.  Rich Rodriguez was fired by Michigan after the game, marking the beginning of the "Brady Hoke Era," as Hoke would be named Rodriguez's replacement as Michigan head coach.

1960 Gator Bowl (January): The 1960 Gator Bowl was a college football bowl game between the Southwest Conference (SWC) co-champion Arkansas Razorbacks and the Georgia Tech Yellow Jackets representing the Southeastern Conference (SEC).  Arkansas defeated Georgia Tech, 14–7, in front of 45,104 spectators.  There were two players named Most Valuable Player: Jim Mooty of Arkansas and Maxie Baughan of Georgia Tech.

1960 Baylor Bears football team: The 1960 Baylor Bears football team represented Baylor University during the 1960 college football season.  The Bears were led by second-year head coach John Bridgers and played their home games at Baylor Stadium in Waco, Texas.  They competed as members of the Southwest Conference, finishing in second and ranked 12th in the final AP Poll with a regular season record of 8–2 (5–2 SWC).  They were invited to the 1960 Gator Bowl, where they lost to Florida, 12–13.

1955 Cotton Bowl Classic: The 1955 Cotton Bowl Classic was a post-season college football bowl game between the Southwest Conference champion Arkansas Razorbacks and the champions of the SEC, the Georgia Tech Yellow Jackets.  Georgia Tech defeated Arkansas, 14-6, in front of 75,550 spectators.  Arkansas would get their revenge in the 1960 Gator Bowl, a 14-7 Hog win.

Supporting paragraphs: 1959 Arkansas Razorbacks football team Frank Broyles
Answer: December 31, 2007