R for small rotations

% Rotation about X axis

In[1]:= rx = {{1, 0, 0}, {0, cx, sx}, {0, -sx, cx}}

Out[1]= {{1, 0, 0}, {0, cx, sx}, {0, -sx, cx}}

% Rotation about Y axis

In[2]:= ry = {{cy, 0, -sy}, {0, 1, 0}, {sy, 0, cy}}

Out[2]= {{cy, 0, -sy}, {0, 1, 0}, {sy, 0, cy}}

% Rotation about Z axis

In[3]:= rz = {{cz, sz, 0}, {-sz, cz, 0}, {0, 0, 1}}

Out[3]= {{cz, sz, 0}, {-sz, cz, 0}, {0, 0, 1}}

% Their product

In[4]:= rx.ry.rz  

Out[4]= {{cy cz, cy sz, -sy}, {cz sx sy - cx sz, cx cz + sx sy sz, cy sx}, 
 
>    {cx cz sy + sx sz, -(cz sx) + cx sy sz, cx cy}}

% Eliminate products of sines.

{1, sz, -sy}, 
{-sz, 1, sx}, 
{sy, -sx, 1}