The sum of all the values of \( \theta \in \left[\frac{\pi}{2}, 2\pi\right] \) satisfying the equation \( \sin^2\theta \tan\theta + \cos^2\theta \cot\theta = \sin 2\theta \) is:
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The equation \( \sin^4\theta + \cos^4\theta = 2\sin^2\theta\cos^2\theta \) is a perfect square. Always look for algebraic identities like \( (a^2-b^2)^2 \) hidden within trigonometric powers to reduce the order of the equation.