If \cos \theta+\sec \theta-2=0, where 0 \leq \theta \lt \frac{\pi}{2}, then what is the value of \cos^4\theta+\sec^4\theta-2?

Explanation

Since \sec \theta = \frac{1}{\cos \theta}, the equation \cos \theta + \frac{1}{\cos \theta} = 2 means (\cos \theta - 1)^2 = 0, so \cos \theta = 1. Substituting \cos \theta = 1 and \sec \theta = 1 into the expression gives 1^4 + 1^4 - 2 = 0.

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