Question 919009
{{{pi/3}}} is {{{60}}} degrees

 Draw a triangle with angles {{{30}}}, {{{60}}}, and {{{90}}}.

 {{{tan(alpha) =opposite/adjacent}}}

Opposite the {{{60}}} degree angle is {{{sqrt(3)}}}. 
Adjacent to the {{{60}}} degree angle is {{{1}}}.

{{{ tan (pi/3) = sqrt(3)/1 = sqrt(3) }}}

or
{{{ tan (60)  = sqrt(3) }}}

{{{14pi/3}}} is {{{14*60 degree=840 degree}}}=>{{{360+360+120}}} degree


{{{tan(360)=0}}}, so {{{tan(14pi/3)=tan(120)}}}

Opposite the {{{120}}} degree angle is {{{sqrt(3)}}}. 
Adjacent to the {{{120}}} degree angle is {{{-1}}}.

{{{tan(120)= -sqrt(3) }}} =>{{{tan(14pi/3)= -sqrt(3)}}}