Tumblr crashed three times while I tried to answer this lovely ask by @floresdoverdepinho - so a normal post it is before I lose my mind completely💻

Hey 👋

The band indeed started into the year 2001 with their Winter leg 2001 of the Sehnsucht tour, which contained concerts and gigs in New Zealand as well as at the Big Day Out festival on different locations all over Australia in January and early February:

including an interview with Paul and Flake on 'Heavy Shift' on the 23.01.2001:

Their last gig during this tour leg was the concert at the Liquidroom venue in Tokyo, 10.02.2001:

Until then, the band was wearing their Sehnsucht outfits, yet already had hairstyles they took with them into Mutter Era. No official dates were planned throughout spring, so the first following appearances of the band during a concert took place in May of 2001, where the members already sported red hair - like Till here in Bielefeld on the 14.05.2001:

Paul and Richard in Hamburg, 16.05.2001:

during the Velodrom gig in Berlin, 18.05.2001:

or in Paris, 9.06.2001:

It appears that the band members didn't let go of the red hair dye simultaneously - Till and Schneider are seen in the end of June/beginning of July with their respective black mohawks (4.07.2001, Los Angeles as well as 5.07.2001, San Francisco):

So the pure red hair era, in which the photoshoot with Scarlet Page must have taken place (she talks about it here) and which was published in the April issue of Kerrang magazine, lasted around three months or a bit more, if we take the active tour months of May to end of June as well as April and possibly March (depending on the date of the shoot) into consideration. In this phase, the photoshoot by Erik Hackenschmidt (where the band wore black uniforms) also must've taken place. The reason for this unifying hair color was simple: "Our new hairstyles, it is just fun. [...] When we are on tour, our crew consists of more than 100 people, and sometimes there are problems with identifying us, the musicians. So to make things easier both for us and the others, we decided to dye our hair." (Polish Playboy).

In the beginning of August, where the band spend time in Mexico, Richard, Flake and Paul still had red hair - during the paintball game (broadcasted on Mexican TV on the 3rd of August) as well as the press conference at the Nikko hotel on the 2nd of August:

About a week later, from the 8th to the 11th of August 2001, the video shoot of 'Ich will' took place in Berlin, where all the members showed up with dark hair:

including Paul, who apparently then went back to red hair (❓) and the infamous era of the red donut ensued, like in the group photoshoot by Mick Hutson in September 2001:

like here in Chicago, 9.10.2001:

or in Estonia, 23.11.2001:

while Schneider ventured out into the boyband-style hair dye, like here on 8.11.2001 at the MTV Awards in Frankfurt: