Solution
$$\left(1+\cot^2\theta\ \right)\left(1-\cos^2\theta\ \right)$$
$$\left(1+\frac{\cos^{^2}\theta\ }{\sin^2\theta\ }\right)\left(1-\cos^2\theta\ \right)$$
$$\left(1+\frac{\cos^{^2}\theta\ }{\sin^2\theta\ }\right)\left(\sin^2\theta\ \right)$$
$$\left(\sin^2\theta\ +\cos^2\theta\ \right)$$
$$1$$
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