45
Evaluate $2\sec^2\theta + 3\text{cosec}^2\theta - 2\sin\theta\cos\theta$ if $\theta = 45^\circ$.
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$$\begin{aligned}& 2 \sec^2 45^\circ + 3 \text{cosec}^2 45^\circ - 2 \sin 45^\circ \cos 45^\circ \\ & = 2(\sqrt{2})^2 + 3(\sqrt{2})^2 - 2(\frac{1}{\sqrt{2}})(\frac{1}{\sqrt{2}}) \\ & = 4 + 6 - 1 = 9\end{aligned}$$