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\tan(\pi +\frac{\pi }{3})=\frac{\tan(\pi )+\tan(\frac{\pi }{3})}{1-\tan(\pi )\tan(\frac{\pi }{3})}
Use \tan(x+y)=\frac{\tan(x)+\tan(y)}{1-\tan(x)\tan(y)} where x=\pi and y=\frac{\pi }{3} to obtain the result.
\frac{0+\tan(\frac{\pi }{3})}{1-0\tan(\frac{\pi }{3})}
Get the value of \tan(\pi ) from trigonometric values table. Replace the value in both the numerator and the denominator.
\frac{0+\sqrt{3}}{1-0\sqrt{3}}
Get the value of \tan(\frac{\pi }{3}) from trigonometric values table. Replace the value in both the numerator and the denominator.
\sqrt{3}
Do the calculations.