A+3C=(π-B-C)+3C=π→2C=B
sinB/sinC=sin(2C)/sinC=2sinCcosC/sinC=2/√3→cosC=⅓√3
cosC=⅓√3→sinC=√(1-⅓)=√⅔→sinB=2sinCcosC=2√⅔·⅓=⅔√2
b/c=2/√3→c=4.5
S=½bcsinA=½·3√3·4.5sin(π-B-C)=6.75√3sin(B+C)
sin(B+C)=sinBcosC+sinCcosB=⅔√2·⅓√3+√⅔·√(1-8/9)
=⅓√6
∴S=6.75√3·⅓√6=6.75√2=