3. (a) Using the identity for \(\cos ( A + B )\), prove that \(\cos \theta \equiv 1 - 2 \sin ^ { 2 } \left( \frac { 1 } { 2 } \theta \right)\).
(b) Prove that \(1 + \sin \theta - \cos \theta \equiv 2 \sin \left( \frac { 1 } { 2 } \theta \right) \left[ \cos \left( \frac { 1 } { 2 } \theta \right) + \sin \left( \frac { 1 } { 2 } \theta \right) \right]\).
(c) Hence, or otherwise, solve the equation $$1 + \sin \theta - \cos \theta = 0 , \quad 0 \leq \theta < 2 \pi$$