Answer:
[tex]{ \boxed{ \mathfrak{ \: answer : \: { \rm{ - \infin}} }}}[/tex]
Step-by-step explanation:
[tex]{ \rm{ \frac{( \cos \theta - \sin \theta) }{ \theta - \frac{\pi}{4} } }} \\ { \tt{ \{lim _{ \theta = \frac{\pi}{4} } \} }} \\ \\ \dashrightarrow \: { \rm{ \frac{( \cos \frac{\pi}{4} - \sin \frac{\pi}{4} ) }{ \frac{\pi}{4} - \frac{\pi}{4} } }} \\ \\ = { \rm{ \frac{0 - 1}{0} }} \\ \\ = { \rm{ \frac{ - 1}{0} }}[/tex]