= tan 20+tan 40( 1+tan 60 * tan 20)

= tan 20+tan 40[tan 60-tan 20]/(tan(60-20)

= tan 20+tan 40(tan 60-tan 20)/tan 40

=tan20 +tan60 -tan20

=tan60

=√3.

Here, the sum and difference angle formula of tangents is used.

tan(A-B)=(tanA-tanB)/(( 1+tanA * tanB)。