Let's boycott Calculus this time! (Part 3)

Geometry Level 4

Find the maximum value of $$\displaystyle \frac{1}{\sin^2x + 3\sin x \cos x +5\cos^2x}$$ correct to 3 decimal places.

If you think that no maximum value exists but a minimum value does, then enter the minimum value. If you think that no global extrema exist for this function, then enter your answer as 666.

Try out Part 1, Part 2.

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