DSolve can't solve this system of differential equation by DSolve. But the basis solution is known. How I can help DSolve to use this basis solution?

WM code:

DSolve[{
x1'[t] == x2[t], 
x2'[t] == 2Cos[t]/(3+2Sin[t])x1[t]-x2[t](3-2Cos[t]+2Sin[t])/(3+2 Sin[t])},
{x1[t], x2[t]},t]

System of equations:

$x_1'(t)=x_2(t)$

$x_2'(t)=\frac{2cos(t)}{3+2sin(t)}x_1(t)-x_2(t)\frac{3-2cos(t)+2sin(t)} {3+2sin(t)}$

Basis solution:

$e^{-t}\{-1,1\}\ and\ \{3-cos(t)+sin(t),sin(t)+cos(t)\}$