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 $2\theta$ ?
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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