- (a) Given that \(\sin ^ { 2 } \theta + \cos ^ { 2 } \theta \equiv 1\), show that \(1 + \tan ^ { 2 } \theta \equiv \sec ^ { 2 } \theta\).
(b) Solve, for \(0 \leqslant \theta < 360 ^ { \circ }\), the equation
$$2 \tan ^ { 2 } \theta + \sec \theta = 1 ,$$
giving your answers to 1 decimal place.