MHB Solve Trig Identity: Tips & Explanation

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To solve the trigonometric identity, visualizing the angles $\theta$ and $2\theta$ through a sketch can be beneficial. This approach helps in understanding the relationships between the angles and their corresponding sine and cosine values. Identifying key points on the unit circle may also clarify the problem. Engaging with visual aids often simplifies complex trigonometric concepts. Utilizing sketches can enhance comprehension and facilitate solving the identity.
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How do I work this out? Can’t seem to get my head around it!
Thanks
 

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Have you made a sketch depicting the respective positions for $\theta$ and $2\theta$ ?
 

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