Encontre os pares $(\alpha ,\beta )\in ]0,\frac{\pi }{2}[\times ]0,\frac{\pi }{2}[$ que satisfazem simultaneamente as equações

$$\{\begin{array}{l}(\mathrm{tg}\alpha +\mathrm{cotg}\beta )\cos \alpha \mathrm{sen}\beta -2{\cos }^2(\alpha -\beta )=-1\\ \sqrt{3}\mathrm{sen}(\alpha +\beta )+\cos (\alpha +\beta )=\sqrt{3}\end{array}$$