If $\tan (\pi \cos \theta)=\cot (\pi \sin \theta)$ then a value of $\cos \bigg( \theta-\large\frac{\pi}{4}\bigg)$ among the following is :

Question

$$(a)\;\frac{1}{2\sqrt 2}  \quad (b)\;\frac{1}{\sqrt 2} \quad (c)\;\frac{1}{2} \quad (d)\;\frac{1}{4}$$