The least value of $f(x)=\tan -1(\sin x+cos x)$ strictly increasing is $$(a)\;\bigg(\frac{\pi}{4},\frac{\pi}{2}\bigg)\qquad(b)\;\bigg(0,\frac{\pi}{2}\bigg)\qquad(c)\;0\qquad(d)\;none\; of\; these.$$

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