Expressions in sin^4 + cos^4 and sin^6 + cos^6 that reduce to a constant

This type of question, asked 3 times: 17 Jul 2023 S4, 18 Jul 2023 S3, 24 Jul 2023 S4. All 3 questions below, oldest first.

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Question 1
17 Jul 2023 S4
58 $\frac{\sin^4\theta + \cos^4\theta}{1 - 2\sin^2\theta \cdot \cos^2\theta} =$
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Question 2
18 Jul 2023 S3
68 $12 (\sin^4 \theta + \cos^4 \theta) + 18 (\sin^6 \theta + \cos^6 \theta) + 78\sin^2 \theta \cos^2 \theta$
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Question 3
24 Jul 2023 S4
63 $\frac{1 + \sin^4\theta + \cos^4\theta}{\cos^2\theta + \sin^4\theta}$
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