Friday Night Lights

Bissinger followed the team for the entire 1988 season. However, the book also deals with â or alludes to â a number of secondary political and social issues existing in Odessa, all of which share ties to the Permian Panthers football team. These include socioeconomic disparity; racism; segregation (and desegregation); and poverty.
The coach, Gary Gaines (Billy Bob Thornton), is constantly in the hot seat. Tied to the successes and failure of the coach and the team in general are the conflicts the players struggle with on and off the gridiron. The coach overuses his star player, running back James "Boobie" Miles (Derek Luke), who gets seriously injured (he tears his ACL, misses the playoffs, and has a limp for the rest of his life). When this happens, sports radios are flooded with calls for Gaines' resignation. Miles' once-arrogant attitude vanishes as he sees his once promising chance of playing big-time college football disappear, and he starts to question his future after he notices his not-so promising academic standing. While recuperating on his uncle's veranda he observes the garbage collectors doing their rounds and gets a glimpse of a somewhat different future he could now face and bursts into tears.
One of the themes of the movie depicts the coach as a father-type figure for the players. For example:

Quarterback Mike Winchell (Lucas Black) struggles with being able to play consistently.
Fullback Don Billingsley (Garrett Hedlund) has a rocky relationship with his alcoholic and abusive father (Tim McGraw). Billingsley silently endures the abuse from his father, who won a state championship at Permian only to find himself unable to get into college and stuck working a dead-end job.
Third-string running back Chris Comer (Lee Thompson Young), who replaces the injured Miles, attempts to get rid of his fear of being hit and getting injured, made worse by seeing his predecessor's season-ending injury. Comer's obsession with fame and recognition also comes at a high price that he is at first not ready to pay.
Safety Brian Chavez (Jay Hernandez) is easily the smartest player on the team and the most confident in his future after high school football. He ends up being academically accepted into Harvard undergraduate and Texas Tech law school.
Coach Gaines triumphs and struggles with winning football games and connecting with his players numerous times during their tumultuous season. His job depends on the Panthers' making the playoffs, and his team is in a three-way tie with two other teams at the end of the regular season. Under Texas rules for ties, the tiebreaker is a coin-toss. Permian gets a spot. Meanwhile, after he drunkenly throws away his championship ring, Don Billingsley's father breaks down and confesses his failures in life cause him to push his son as harshly as he does, pointing out that he wants his son to at least have one big moment of triumph before dealing with the harshness of the real world. The team makes it to the finals, where they narrowly lose against powerhouse Dallas Carter High School. The movie ends with the coach removing the departing seniors from the depth chart on his wall. Notably, the depth chart has "Case" at quarterback. This refers to Permian's real-life backup quarterback in 1988, Stoney Case, who would go on to lead Permian, along with Chris Comer, to the 5A state title the following year, and still later make it to the NFL.

Question: What does Don Billingsley drunkenly do?
Answer: Throw away his championship ring