MHB Solving for $\theta$: Which Value is a Counterexample?

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The discussion centers on identifying a counterexample to the identity sin²θ + cos²θ = tan²θ. Participants explore substituting values for θ, specifically pi/4, 5pi/4, and pi/3, to test the validity of the equation. It is concluded that the equation does not hold true universally, as sin²θ + cos²θ equals 1, while tan²θ does not equal 1 for all values of θ. Therefore, the original statement is not an identity. The key takeaway is that there are specific values of θ that demonstrate this discrepancy.
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Which value for $\theta$ is a counterexample to sin^2$\theta$+cos^2$\theta$=tan^2$\theta$ as an identity?

a) pi/4
b) 5pi/4
c) pi/3
d) It is an identity

So I tried subbing in each value (a, b, c) in as x and then finding the exact value from that but I'm not getting it.
 
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Well, you know that $\sin^2\left({x}\right)+\cos^2\left({x}\right)=1$, so the statement you're given above is not an identity, since it does not hold true that $\tan^2\left({x}\right)=1$ for all values of $x$. :)
What can you deduce when you put the numbers on the right side, $\tan^2\left({x}\right)$? (Tongueout)
 
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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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