While I sometimes advise obtaining certificates on overprinted stamps, expertization is not necessary in this case, because there is not enough of a price difference between the basic stamps and the surcharges to make it worthwhile.
In 1964, Tanganyika joined Zanzibar to form the United Republic of Tanganyika and Zanzibar, which changed its name to the United Republic of Tanzania in 1965. While it is likely that in the near-term, British Commonwealth collectors will generate most of the demand for stamps of Zanzibar, should a significant stamp collecting community develop within Tanzania, the undervalued stamps of the former protectorate will skyrocket.
Tanzania has a population of about 43 million, and its economy is mostly based on agriculture, which accounts for more than half of the GDP, provides about 75% of exports, and employs approximately 75% of the workforce. Topography and climate, though, limit cultivated crops to only 4% of the land area. The nation has many natural resources including minerals, natural gas, and tourism, and the government has instituted policies to promote development of these sectors. Annual GDP growth has averaged about 6.5% over the last 5 years.