Do changing opt=modredundant to opt in Gaussian makes geometry optimization not to take into account frozen angles?
The following illustrates the use of modredundant in a simple optimization (water angle at fixed bond lengths).
Input:
# B3LYP/6-31G(d) Opt=ModRedundant

test to see how to freeze coordinates

0 1 
H     0.0 0.0 0.0
O     1 1.0
H     2 1.2 1 105.0 

1 2 F
2 3 F

Optimized internal coordinates:
                           ----------------------------
                           !   Optimized Parameters   !
                           ! (Angstroms and Degrees)  !
 --------------------------                            --------------------------
 ! Name  Definition              Value          Derivative Info.                !
 --------------------------------------------------------------------------------
 ! R1    R(1,2)                  1.0            -DE/DX =   -0.0225              !
 ! R2    R(2,3)                  1.2            -DE/DX =   -0.1043              !
 ! A1    A(1,2,3)               99.0431         -DE/DX =    0.0                 !
 -------------------------------------------------------------------------------

Note the angle was not constrained so the final value differs from the input.
Now change the route to
# B3LYP/6-31G(d) Opt

and the output changes to
                       ----------------------------
                           !   Optimized Parameters   !
                           ! (Angstroms and Degrees)  !
 --------------------------                            --------------------------
 ! Name  Definition              Value          Derivative Info.                !
 --------------------------------------------------------------------------------
 ! R1    R(1,2)                  0.9687         -DE/DX =    0.0                 !
 ! R2    R(2,3)                  0.9688         -DE/DX =    0.0                 !
 ! A1    A(1,2,3)              103.6489         -DE/DX =    0.0                 !
 -------------------------------------------------------------------------------

So sure enough, removing modredundant loosens restraints under the optimization.