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\subsubsection{Lemma 2}  \textbf{Claim}: $\frac{1}{\cos x - \sin x}$ is monotone decreasing for $x\in (0, 2\pi/7) \ \square$.  \textbf{Pf}: $\frac{d(\cos x - \sin x)}{dx}=-(\sin x + \cos x) < 0$ for $x\in (0, \pi/4)$ therefore $\cos x - \sin x$ is monotone decreasing on this domain. As such, $\frac{1}{\cos x - \sin x}$ is monotone increasing.  \subsubsection{Main Proof}  \textbf{Pf}: $\frac{d(\cos x - \sin x)}{dx}=-(\sin x + \cos x) < 0$ for $x\in (0, \pi/4)$ therefore $\cos x - \sin x$ is monotone decreasing on this domain. As such, $\frac{1}{\cos x - \sin x}$ is monotone increasing.