7. (a) Prove the identity \(\frac { \cos x } { \sec x + 1 } + \frac { \cos x } { \sec x - 1 } \equiv 2 \cot ^ { 2 } x\)
[0pt] [3 marks]
(b) Hence, solve the equation $$\frac { \cos \left( 2 \theta + \frac { \pi } { 3 } \right) } { \sec \left( 2 \theta + \frac { \pi } { 3 } \right) + 1 } = \cot \left( 2 \theta + \frac { \pi } { 3 } \right) - \frac { \cos \left( 2 \theta + \frac { \pi } { 3 } \right) } { \sec \left( 2 \theta + \frac { \pi } { 3 } \right) - 1 }$$ in the interval \(0 \leq \theta \leq 2 \pi\), giving your values of \(\theta\) to three significant figures where appropriate.
[0pt] [5 marks]
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