"Al-Takeyya is based on the following Quranic verse:...."
Nope, the verse you cite says nothing about lying, whoever you are getting your info from is simply wrong - Perhaps you may want to look at a different translation http://etext.virginia.edu/etcbin/ot2www-koran?specfile=/lv2/english/relig/koran/www/koran.o2w&act=surround&offset=82561&tag=Koran.003&query=3:28
But...you may want to look at -
"Any one who, after accepting faith in Allah, utters Unbelief, except under compulsion, his heart remaining firm in Faith - but such as open their breast to Unbelief, on them is Wrath from Allah, and theirs will be a dreadful Penalty." Surah 16: 106
This allows a believer under compulsion to tell falsehoods.
RS, live & learn! near the bottom of the page & plz don't bother responding ! TIA
http://www.islamreview.com/articles/lying.shtml