If $$\sin \alpha+ \cos \beta= 2;$$$$\left( {{0^ \circ } \leqslant \beta< \alpha\leqslant {{90}^ \circ }} \right){\text{,}}$$then $${\text{sin}}\,{\left( {\frac{{2\alpha+ \beta }}{3}} \right)^ \circ }$$is?

• A. ${\text{sin }}\frac{\alpha }{2}$$
• B. $\cos \frac{\alpha }{3}$$
• C. ${\text{sin }}\frac{\alpha }{3}$$
• D. $\cos \frac{{2\alpha }}{3}$$