Verified answer

[tex] \sin( \frac{\pi}{3} ) - \cos( \frac{\pi}{3} ) + \tan( \frac{\pi}{4} ) = \frac{ \sqrt{3} }{2} - \frac{1}{2} + 1 = \\ = \frac{ \sqrt{3} - 1 + 2}{2} = \frac{ \sqrt{3} + 1 }{2} [/tex]