Mr Tanaka is the second minister to step down in the year since he took office.
Tanaka spoke to Correspondent Murakami Mutsuko about the difficulty of refreshing politics in Japan.
In return, ministry officials have briefed him on policy, while keeping Mrs Tanaka in the dark.
Miss Domoto, Mr Tanaka, Mr Ishihara and the other unruly governors owe their success to their independence.
In 1974, Japanese Prime Minister Kakuei Tanaka resigned following allegations of irregularities in his private business affairs.
He has blocked Mrs Tanaka's attempts to move her enemies in the foreign ministry to new jobs.
Tanaka is aware of the comparisons to Facebook's Mark Zuckerberg, and not just in his dress sense.
But now the old manipulators have gone: Tanaka, Kanemaru, in disgrace in 1996, Obuchi, prematurely, and now Takeshita.
Japan's top government spokesman, Chief Cabinet Secretary Osamu Fujimura, said Mr Tanaka had stepped down due to ill health.
Tanaka believes a key weakness of corporate Japan has been its insular attitude.
Tanaka Kakuei was prime minister from 1972 to 1974 and stepped down under the cloud of a bribery scandal.
He remained, though, a power in politics, in the manner of the deposed Kakuei Tanaka, deciding who should rule.
The prize for mass spectrometry is shared by John Fenn and Koichi Tanaka.
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Dr Fenn and Dr Tanaka have won their awards for improvements to it.
ECONOMIST: This year, the Nobel authorities have shown a deft touch
Stefan Szymanski, of Tanaka Business School at Imperial College in London, also doubts the economic claims made for such events.
Chikai Tanaka, an analyst at Nomura Securities in Japan, said he obtained that figure from a meeting with Trend Micro.
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Mrs Tanaka landed the foreign ministry because her support for Mr Koizumi was crucial in lifting him to power in April.
Magosaki is plainly of the latter camp, in which he also identifies prime ministers Tanaka Kakue, Miyazawa Koichi, and Hatoyama Yukio.
Takeshita's predecessor as a shadow shogun, Tanaka Kakuei, also had a short tenure as premier and resigned because of various scandals.
Married (to another Diet member) with three children, Tanaka, 55, connects with ordinary folk as a housewife who bicycles to the supermaket.
Mrs Tanaka appealed to Mr Koizumi, who has conveniently been travelling abroad.
The father of Makiko Tanaka, another prominent member, was once prime minister.
Instead, they snipe at his foreign minister, the redoubtable Makiko Tanaka, a woman whose outspokenness is unsettling those who prefer Japan's usual ultra-cautious diplomacy.
Mr Tanaka's administration in Nagano has become so transparent that he even sits behind glass walls, through which voters can see their governor at work.
It's easy to lay blame at the feet of the politicians but Japan is a democracy and so everyone has to share responsibility, believes Tanaka.
In Nagano, Mr Tanaka won with the support of citizens' groups that opposed a dam the construction ministry wanted built against the wishes of local residents.
"It's a grave issue that troubles occur so frequently, " said Shunichi Tanaka, chairman of the Nuclear Regulation Authority, at a news conference in Tokyo on Wednesday.
When Kakuei Tanaka, the boss of their faction, was weakened after being accused, among other misdeeds, of taking bribes, the two men set about taking over.
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