You you can use VMD's tcl scripting to get phi/psi angles. Bellow is a script originally posted here, but with few modifications.

mol new "1abc.pdb" waitfor all

set fp [ open "phi-psi.dat" w ] 
set sel [ atomselect $mol "alpha" ] 
set n [ molinfo $mol get numframes ] 
for {set i 0 } { $i < $n } { incr i } { 
    $sel frame $i 
    $sel update 
    puts $fp "\# frame: $i" 
    set a [ $sel num ] 
    for {set j 0 } { $j < $a } { incr j } { 
        puts $fp "[expr $j + 1] [lindex [$sel get {resname phi psi}] $j]" 
    } 
} 
$sel delete 
close $fp 
exit

Have you tried SSTRUC part of JOY package:

Here is first few lines of output for PDB ID: 2DXL. It basically generates this complete file for a given protein structure. You can then parse the output file for residues/regions.

Secondary structure calculation program - copyright by David Keith Smith, 1989
2DXL.atm                                                    
      HYDROLASE  MOL_ID: 1;  MOL_ID: 1;  
Sequence length - 1626
            A       A K K                                                                        hydrogen bonding             Ooi's
strk chain/ l amino u & S structure   bridge        dihedral angles                     donor    acceptor   donor    acceptor  N  N
num  seq.no t acids t S + patterns   partners    phi    psi  omega  alpha kappa   tco to/energy fr/energy to/energy fr/energy  8 14
   1 A   1    MET M     e              0    0  999.9  123.3  172.5  999.9 999.9 999.9    0   .0  242 -2.1    0   .0    0   .0  9 38
   2 A   2    LEU L   E E  AA     -  241    0 -129.1  120.1 -178.7 -174.5 999.9 169.0    0   .0   43 -3.3    0   .0   44 -1.1 11 43
   3 A   3    LEU L   E E  AAb    -  240   44 -116.7  133.3  170.7 -151.1  18.7 160.3  240 -3.2  240 -2.6    0   .0    5  -.7 12 57
   4 A   4    ALA A   E E  AAb    -  239   45  -98.4  115.0 -174.0 -166.1  22.9 157.6   44 -2.3   46 -2.7    0   .0    6  -.6 13 61
   5 A   5    HIS H   E E  AAb    +  238   46 -113.9  111.2  176.0  163.3  15.5 155.4  238 -3.5  238 -2.5    3  -.7    0   .0 12 74
   6 A   6    ILE I   E E  A b    -    0   47 -118.5  165.3 -174.2 -171.0  11.8 143.3   46 -3.1   48 -1.7    4  -.6    0   .0 17 78
   7 A   7    SER S               +    0    0 -152.5  158.5  166.2   24.5  49.7 168.3    0   .0  215 -1.5    0   .0    0   .0 17 76
   8 A   8    ASP D               +    0    0   54.9   54.3 -179.7  167.0  51.6  28.6    0   .0  216  -.5    0   .0    0   .0 16 78
   9 A   9    THR T               -    0    0  -69.5  -32.1  175.2 -161.9  22.4  38.4    0   .0    0   .0    0   .0    0   .0 14 79

============== Removed for brevity =======================

maybe you want to have a look at p3d

I believe that the 'press' R package allows calculation of psi-phi angles from a PDB file

You can easily do this in BioJava as well if it suits you better.

Here's a code example: http://www.biojava.org/docs/api/org/biojava/bio/structure/Structure.html (See 'How can I calculate Phi and Psi angles of AminoAcids?')