If boost matrices are always symmetric, why is it not so in my example?

Consider two consecutive boosts in $2+1$ dimensional spacetime, the first along the $x$-axis and the second along the $y$-axis. The net transformation is $$B_y(theta_2)B_x(theta_1)=begin{pmatrix}
coshtheta_2 & 0 & -sinhtheta_2\
0 & 1 & 0\
-sinhtheta_2 & 0 & coshtheta_2
end{pmatrix}begin{pmatrix}
coshtheta_1 & -sinhtheta_1 & 0\
-sinhtheta_1 & coshtheta_1 & 0\
0 & 0 & 1
end{pmatrix}hspace{1.89cm}\=begin{pmatrix}
coshtheta_2coshtheta_1 & -coshtheta_2sinhtheta_1 & -sinhtheta_2\
-sinhtheta_1 & coshtheta_1 & 0\
-sinhtheta_2coshtheta_1 & sinhtheta_2sinhtheta_1 & coshtheta_2
end{pmatrix}.$$ Since the product boost $B_y(theta_2)B_x(theta_1)$ can always be written as the product of a rotation and a boost, I can write $B_y(theta_2)B_x(theta_1)=R_z(phi)B_{hat n}(theta)$. Here, $R_z(phi)$ is the rotation matirx in the $xy$ plane and $B_{hat n}(theta)$ is some boost matrix. By brute force calculation, I find that $$B_{hat n}(theta)=R_z^{-1}(phi)B_y(theta_2)B_x(theta_1)\=left(
begin{array}{ccc}
1 & 0 & 0 \
0 & cosphi & sinphi\
0 & -sinphi & cosphi\
end{array}
right).left(
begin{array}{ccc}
coshtheta _2 & 0 & -sinhtheta _2\
0 & 1 & 0 \
-sinhtheta _2 & 0 & coshtheta _2\
end{array}
right).left(
begin{array}{ccc}
coshtheta _1 & -sinhtheta _1 & 0 \
-sinhtheta _1 & coshtheta _1 & 0 \
0 & 0 & 1 \
end{array}
right)\
={small left(
begin{array}{ccc}
coshtheta_1coshtheta_2 & -coshtheta_2 sinhtheta_1 & -sinhtheta_2\
-cosphisinhtheta_1-coshtheta_1 sinphisinhtheta_2 & cosphicoshtheta_1+sinphisinhtheta _1sinhtheta_2 & coshtheta _2sinphi\
sinphisinhtheta _1-cosphicoshtheta _1sinhtheta _2 & cosphisinhtheta _1sinh theta _2-coshtheta _1 sin phi & cosphicoshtheta_2\
end{array}
right)}$$

If boost matrices are always symmetric (the general form can be found here), why is $B_{hat n}(theta)$ calculated above is not symmetric? A pointing out my mistake will also be much appreciated.