content_image/307285.jpg content_image/307286.jpg content_image/307287.jpg content_image/307288.jpg content_image/307289.jpg
and 

From Eq. (F.46) we find 

<img src='content_image/307285.jpg'>

<img src='content_image/307286.jpg'>

<img src='content_image/307287.jpg'>

where we have used the vector identity ( ⃗ a × ⃗ b ) · ( ⃗ c × ⃗ d ) = ( ⃗ a · ⃗ c )( ⃗ b · ⃗ d ) − ( ⃗ a · ⃗ d )( ⃗ b · ⃗ c ), and 

Plugging these pieces into Eq. (F.21) we find that 

<img src='content_image/307288.jpg'>

<img src='content_image/307289.jpg'>

First let’s prove that the coefficient of the cos term is 0. It’s clear that the 

