Wrong calculation of geographic coordinates from rectangular coordinates in Transverse Mercator projection

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This issue is a sequel and further development of issue No. 180 
(http://code.google.com/p/androzic/issues/detail?id=180). The effect of track 
shift still remains in last version of Androsic, but previous diagnosis was 
wrong.

What steps will reproduce the problem?

1.Download archive (http://www.uazpatriot.ru/kom/Test.zip) and open files 
N-36-023_ozf.map and N-36-023_ozf_degr.map.
2.Open file myTrack.plt
3.Look at the difference between track position in these two maps.

What is expected? What do you get instead?

It is expected that track position in these two maps will be identical (see 
screenshots for OziExplorer OZI_geogr.jpg and OZI_rectang.jpg). Instead, we 
have appreciable map shift in the case of the map N-36-023_ozf.map (see 
screenshots Androzic_geogr.jpg and Androzic_rectang.jpg).

What version of the product are you using?

Androzic 1.2.3, OziExplorer for Android 1.10, Android 2.3.5, Samsung Galaxy S 
II.

The map N-36-023_ozf_degr.map was prepared from N-36-023_ozf.map via simple 
change of calibration points specified in rectangular units to corresponding 
degree (geographic) units. Pixel position and corner position remained 
untouched.
Notice here that coordinates of calibration points and map corners are indeed 
equal.
We can see that after internal (by Androsic) conversion of calibration points 
coorinates from rectangular to geographic, latitudes of calibration points 
differ from corners coordinates in the 3rd decimal place! And the differences 
of longitudes are in 4th decimal place (see screenshot Rectangular.jpg). On the 
contrary, when we take the map N-36-023_ozf_degr.map (with "geographic" 
calibration) these differences  not exceed several units in 5th decimal place 
(see Geographic.jpg).
Now we can draw a conclusion that this map shift is due to wrong calculation of 
geographic coordinates from rectangular ones. The most likely reason of this is 
a possible mistake in formula for latitude (or maybe longitude too).

Original issue reported on code.google.com by uazi...@gmail.com on 19 Jan 2012 at 6:45

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Ошибка дожила и до версии 1.4.
Прискорбно. 

Original comment by uazi...@gmail.com on 15 Feb 2012 at 6:05

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Спасибо за тестовый набор карт, я нашёл, 
наконец, проблему, исправление войдёт в 
следующую версию.

Original comment by novikov on 16 Feb 2012 at 1:10

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Original comment by uazi...@gmail.com on 16 Feb 2012 at 1:35

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Спасибо! Все прекрасно работает в 1.4.2

Original comment by uazi...@gmail.com on 23 Feb 2012 at 6:16