6 The first, third and fourth terms of an arithmetic progression are \(u _ { 1 } , u _ { 3 }\) and \(u _ { 4 }\) respectively, where \(u _ { 1 } = 2 \sin \theta , \quad u _ { 3 } = - \sqrt { 3 } \cos \theta , \quad u _ { 4 } = \frac { 7 } { 2 } \sin \theta\), and \(\frac { 1 } { 2 } \pi < \theta < \pi\).
- Determine the exact value of \(\theta\).
- Hence determine the value of \(\sum _ { r = 1 } ^ { 100 } u _ { r }\).