How to find Rotation Matrix for a Given Position?

The position of any point in space can be calculated via rotation+displacement. But how can we calculte if the position is known, and rotation matrix is desired to be found?

My code is below.

close all;clear all;clc;
rb=30;rp=15;
t=[0,0,60]';
deg120=120*pi/180;deg60=60*pi/180;
p1=[rp*cos(deg60),             rp*sin(deg60),             0]';
p3=[rp*cos(deg60+deg120),      rp*sin(deg60+deg120),      0]';
p2=[rp*cos(deg60+2*deg120),    rp*sin(deg60+2*deg120),    0]';
% p1=[7.50,  12.9904, 0]'
% p2=[7.50, -12.9904, 0]'
% p3=[-15,    0,      0]'

alpha=0*pi/180;beta=0*pi/180;gamma=0*pi/180;
Rx=[1   0               0;
    0   cos(alpha)  -sin(alpha)
    0   sin(alpha)  cos(alpha)];
Ry=[cos(beta)   0   sin(beta)
    0           1       0
    -sin(beta) 0   cos(beta)];
Rz=[cos(gamma)  -sin(gamma)   0
    sin(gamma)  cos(gamma)    0
    0           0           1];
R=Rz*Ry*Rx;  P1=R*p1+t;P2=R*p2+t;P3=R*p3+t;

% -------Second part of the code (after some rotation)
alpha_new=20*pi/180;beta_new=20*pi/180;gamma_new=20*pi/180;

Rx_new=[1   0               0;
    0   cos(alpha_new)  -sin(alpha_new)
    0   sin(alpha_new)  cos(alpha_new)];
Ry_new=[cos(beta_new)   0   sin(beta_new)
    0           1       0
    -sin(beta_new) 0   cos(beta_new)];
Rz_new=[cos(gamma_new)  -sin(gamma_new)   0
    sin(gamma_new)  cos(gamma_new)    0
    0           0           1];
R_new=Rz_new*Ry_new*Rx_new;
P1_new=R_new*p1+t;P2_new=R_new*p2+t;P3_new=R_new*p3+t;

For the code above, imagine that we know P1_new, P2_new, P3_new, and t. Therefore, we want to find R_new rotation matrix, and also alpha_new, beta_new, gamma_new angles. (They are set to 20degrees. But imagine that we don't know it yet.)

How can I find alpha_new, beta_new, gamma_new angles? Thanks in advance.