Computing Euler angles from a rotation matrix is straightforward once you set a convention. Indeed is possible to compute an entire different set of angles that defines a rotation when you change axis. In this case I use the aeronautical notation, with pitch, yaw and roll as a plane taking off.

% Returns euler angles in radians given a wanted convention, implementation from GPU Gems IV and
% from Eigen libraries

function [x,y,z] = eulerAngles(R,a0,a1,a2)

res=zeros(1,3);
odd=-1;
if ( mod(a0+1,3)==a1 )
    odd=0;
else
    odd=1;
end

i = a0;
j = mod((a0 + 1 + odd),3);
k = mod((a0 + 2 - odd),3);

i=i+1;
j=j+1;
k=k+1;

if (a0==a2)
    s = norm([ R(j,i),R(k,j) ]);
    y = atan2(s, R(i,i));
    if (s > eps)
        x = atan2(R(j,i), R(k,i));
        z = atan2(R(i,j),-R(i,k));
    else
        x = 0.0;
        if (R(i,i)>0)
            z=atan2(-R(k,j), R(j,j));
        else
            z=-atan2(-R(k,j), R(j,j));
        end
    end
else
    c = norm([ R(i,i),R(i,j)] );
    y = atan2(-R(i,k), c);
    if (c > eps)
        x = atan2(R(j,k), R(k,k));
        z = atan2(R(i,j), R(i,i));
    else
        x = 0.0;
        if (R(i,k)>0)
            z=atan2(-R(k,j), R(j,j));
        else
            z=-atan2(-R(k,j), R(j,j));
        end
    end
end

res=[x,y,z];
if (~odd)
    res = -res;
end

x=res(1);
y=res(2);
z=res(3);

Computing Euler angles from 3x3 rotation matrix in Matlab

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