Question

find the exact value of the following expression.
\\( \frac { \tan \frac { \pi } { 3 } + \tan \frac { 2 \pi } { 3 } } { 1 - \tan \frac { \pi } { 3 } \tan \frac { 2 \pi } { 3 } } \\)
\\( \frac { \tan \frac { \pi } { 3 } + \tan \frac { 2 \pi } { 3 } } { 1 - \tan \frac { \pi } { 3 } \tan \frac { 2 \pi } { 3 } } = \square \\)
(simplify your answer, including any radicals. use integers or fractions for any numbers in

Explanation:

Step1: Recall the tangent addition formula

The formula for \(\tan(A + B)=\frac{\tan A+\tan B}{1 - \tan A\tan B}\). Let \(A=\frac{\pi}{3}\) and \(B = \frac{2\pi}{3}\).

Step2: Calculate \(A + B\)

\(A + B=\frac{\pi}{3}+\frac{2\pi}{3}=\pi\)

Step3: Find the value of \(\tan(A + B)\)

Since \(\tan(\pi)=0\)

Answer:

\(0\)