The Fast and the Furious: Tokyo Drift was the third installment in the franchise though its placement in the FF storyline would later be altered after the movie's failure at the box office. The main reason for its limited success, aside from being a bad movie, is likely due to the filmmakers making the spectacularly bad decision to use a completely different set of characters. It's as if they found a script about racing and thought cars and the Fast and the Furious title would be enough to please people.
The movie opens at a high school where Sean (Lucas Black), our hero, has a run-in with Clay (Zachery Ty Bryan), a stereotypical idiot football player because his girl Cindy (Nikki Griffin) says "hello" to Sean. They decide to settle things by racing. To make things more enticing or more likely to keep herself as the center of attention, Cindy offers herself as the prize to the winner, although that's not really a prize for Clay since he already has her, but then he's not a mathlete so thinking isn't his strong suit. They race at an incomplete housing development without any real sense of structure to the race track, so it's not clear where the finish line is.
The three get into trouble with the law as a result. Clay and Cindy get off easy because they are rich, white kids while Sean is seen as the problem. His mom (Lynda Boyd) comes to get him and she gives off an odd vibe as her desire to do anything to get Sean off seems to indicate she'd be willing to get a police officer off as well. Sean and his mom have had to move a few times because of his driving transgressions, so in order to avoid jail this time and because she's tired of relocating, Sean is shipped off to Tokyo where his dad, Navy Lieutenant Boswell (Brian Goodman), is stationed.
In Tokyo high school, Sean meets Twinkie (Bow Wow), an American hustler of questionable merchandise, and Neela (Nathalie Kelley), an Australian gal who is dating Takashi (Brian Tee), the local drift-racing king, who is also referred to as DK. Even more troubling is he's the nephew of Yakuza boss Kamata (Sonny Chiba). As explained on wikipedia, “drifting is a driving technique where the driver intentionally oversteers, causing loss of traction in the rear wheels, while maintaining control from entry to exit of a corner. A car is drifting when the rear slip angle is greater than the front slip angle, to such an extent that often the front wheels are pointing in the opposite direction to the turn (e.g. car is turning left, wheels are pointed right or vice versa).” Naturally, Sean and Takashi clash over Neela, and Sean's first attempt at drifting to show off their manliness is horrendous, resulting in a severely damaged car, which belongs to Han (Sung Kang), DK's business partner. To pay Han back for the damage, Sean works for him.
When it is discovered that Han has been cheating Takashi and the Yazuka, a major car chase through Tokyo commences that offers one of the movie's better action sequences. Later, Sean tries to make peace by suggesting to Kamata a “loser leave town” race, which Kamata volunteers Takashi for. It occurs on a mountain road and is shot at night, so visually the sequence is very underwhelming. DK repeatedly tries to run Sean off the road, so it makes no sense why he keeps pulling ahead of him. What does make sense is who the winner is, which is was never in doubt.
Drift racing is an intriguing concept, but director Justin Lin and his crews, both camera and stunt, failed to make a majority of the movie's action scenes exciting, which they needed to accomplish in order to keep people engaged during the boring exposition scenes and considering the precedent of the previous two movies. If those hadn't been so successful that they could absorb Tokyo Drift's poor performance, this could have been the end of the franchise, or at least sent it into a long dormancy.
I am just making my way through the FF franchise and am not aware of the stories, so I kept waiting to see how Tokyo Drift connected to the FF world, but as it progressed all it offered was external things such as racing, a dumb script, and terrible music choices. That is until the epilogue when a mysterious racer shows up claiming to know Han and wanting to take on the new drift king. It felt tacked on like an afterthought, but then the whole script wasn't well-thought through.
No matter where this chapter falls in the Fast and the Furious timeline, I would recommend drifting right on by it.