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If $A+B+C=\frac{\pi}{2}$,then $\sqrt{2} \cos \left(\frac{\pi}{4}-A\right)+\sqrt{2} \cos \left(\frac{\pi}{4}-B\right)+\sqrt{2} \cos \left(\frac{\pi}{4}-C\right)+1=$

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Let $f(\theta) = (1 + \sin^2 \theta)(2 - \sin^2 \theta)$. Then, for all values of $\theta$:

If $a$,$b$,and $c$ are non-zero real numbers,then the minimum value of the expression $\left( \frac{(a^4 + a^2 + 1)(b^4 + 7b^2 + 1)(c^4 + 11c^2 + 1)}{a^2 b^2 c^2} \right)$ is

If $A + B + C = 180^\circ$,then $\frac{\sin 2A + \sin 2B + \sin 2C}{\cos A + \cos B + \cos C - 1} = $

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