In Eq. (24) replace sin phi by sin theta in the first term on the right hand side. In Eq. (27) replace sin phi by sin theta in the first term on the left hand side. These are just typo’s which do not affect the result for the spin connection. The were caused by the fact that VAPS interchanges theta and phi in its use of spherical polar coordinates. Note 369(4) uses the standard notation.