$$Var(X+Y+Z)=Var(X)+Var(Y)+Var(Z)+2Cov(X,Y)+2Cov(X,Z)+2Cov(Y,Z)$$ And since X, Y, and Z have the same distribution $$Var(X+Y+Z)=3Var(X)+2Cov(X,Y)+2Cov(X,Z)+2Cov(Y,Z)$$
$$Var(X+Y+Z)=Var(X)+Var(Y)+Var(Z)+2Cov(X,Y)+2Cov(X,Z)+2Cov(Y,Z)$$ And since X, Y, and Z have the same distribution $$Var(X+Y+Z)=3Var(X)+2Cov(X,Y)+2Cov(X,Z)+2Cov(Y,Z)$$