Verify the Identity $$\tan \left( x - \frac { \pi } { 4 } \right) = \frac { \tan x - 1 } { 1 + \tan x }$$

Verify the identity.
- $$\tan \left( x - \frac { \pi } { 4 } \right) = \frac { \tan x - 1 } { 1 + \tan x }$$