Solution
$$1 + \tan ^2 \theta = \sec ^2 \theta$$
$$1 + \cot ^2 \theta = \csc ^2 \theta$$
So, the given fraction becomes,
$$\frac{1}{\sec ^2 \theta} + \frac{1}{\csc ^2 \theta} = \sin^2\theta + \cos^2 \theta = 1$$
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