How do I do the math necessary to make these five matrices multiplied together equal the result shown?

Question

I'm currently studying the math involved with rotating vertices around an arbitrary axis in 3D space. For this, I have found the following page to be very helpful:
http://inside.mines.edu/~gmurray/ArbitraryAxisRotation/ArbitraryAxisRotation.html

Conceptually, I get everything, however, when I try to multiply Txz-1, Tz-1, Rz(θ), Tz and Txz together, I can't get the result shown for the first matrix in 5.1.

The matrix for Txz is as follows:

The matrix for Tz is as follows:

And the matrix for Rz(θ) is as follows:

While not shown on the page, the matrices for Txz-1 and Tz-1 are easy enough to generate, but with all that said, could someone please give me some advice on how the author of the page is able to multiply those five matrices together and get the following result?

Thank you very much.