Let
α
T
and
α
Z
, respectively, be the angles of
X
and
C
for
T
and
Z
, respectively. Prove that
sin
(
α
Z
/
2
)
=
sin
(
α
T
/
2
)
β
1
−
e
v
In this case the factor of contraction also depends on the direction of
X
!
Again, we have
−
⟨
X
,
T
⟩
=
−
⟨
C
,
T
⟩
=
1
and
−
⟨
X
,
Z
⟩
=
β
(
1
−
e
v
)
,
−
⟨
C
,
Z
⟩
=
β
; by
(???)
we thus obtain the result.