n=5

e[n_,i_] := IdentityMatrix[n][[i]];

R[n_, t__] := Module[
{M=IdentityMatrix[n],k=0},
Do[
M= M.RotationMatrix[{t}[[++k]],{e[n,i],e[n,j]}],
{i,n-1},{j,i+1,n}
];
M
]

R[3,0.1,0.2,.3] // MatrixForm