Rotating an elastic tensor from 100 to 711 axis

[mathgirlie]

TL;DR Summary

Rotating an elastic tensor from 100 to 711 axis

I have the elastic tensor for a material where C11 aligns with the 100 axis , C22 aligns with the 010 axis and C33 aligns with the 001 axis. I want to rotate it so the the new axis are for a configuration with an axis along 711. How do I come up with the rotation matrix to do this?