If \frac{\cos \theta}{1 - \sin \theta} + \frac{\cos \theta}{1 + \sin \theta} = 4, then which one of the following is a value of (\tan^2 \theta + \cot^2 \theta) ?

Explanation

Simplifying the given equation yields \frac{2\cos\theta}{\cos^2\theta} = 4, so \cos\theta = \frac{1}{2}, which means \theta = 60^\circ. Therefore, \tan^2 60^\circ + \cot^2 60^\circ = 3 + \frac{1}{3} = \frac{10}{3}.

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