This tactic is also part of the alternate strategies video.
When Takamoto moves to the statue next to the one where Lara is hiding, step out just far enough to see Takamoto but not so far that he retaliates. (If he attacks, move back behind the statue.)
Switch to manual targeting and aim for the top of the wall behind Takamoto.
Without exiting manual aim mode, hold the grenade button for several seconds and then release. (This makes the grenade go farther.)
If you've aimed well, the grenade will bounce off the wall and land behind him.
He makes no effort to dodge, and it does a ton of damage. If he's still alive and hasn't run off, try another grenade. Otherwise, run to the next statue—on the opposite side of the walkway from him—and take cover. Then continue fighting as before.
[Part 1 | Part 3 | Return to Japan Walkthrough]