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hi,
   I recommend you to read three papers about  phase transition:(1) Phases of
vanadium under pressure investigated from first principles.J. Phys.: Condens.
Matter 20 (2008) 275218.
(2) On the importance of the free energy for elasticity under pressure.J.
Phys.: Condens. Matter 14 (2002) L525–L528. (3) Comment on 'On the importance
of the free energy for elasticity under pressure'.Journal of Physics:Condensed
Matter.2004,16(47):8783-8786.
The three papers, especialy (2)&(3), have clear explanation of computation
procedures of phase transiton.
   And if you think the computation of different angles is boring, just write 
a
shell script to help you. That is very easy, i am sure you can make it.

regards
J J Wang