If each $$\alpha,\beta$$ and $$\gamma$$ is a positive acute angle such that $$Sin(\alpha+\beta-\gamma)=\frac{1}{\sqrt{2}},Cosec(\beta+\gamma-\alpha)=\frac{2}{\sqrt{3}}$$ and $$tan(\gamma+\alpha-\beta)=\frac{1}{\sqrt{3}}$$. What are the values of $$\alpha,\beta,\gamma$$?

if $$Sin(\alpha+\beta-\gamma)=\frac{1}{\sqrt{2}} $$then $$\alpha+\beta-\gamma$$ = 45°  ...(1)

if $$Cosec(\beta+\gamma-\alpha)=\frac{2}{\sqrt{3}}$$ then $$\beta+\gamma-\alpha$$ = 60°   ...(2)

if $$tan(\gamma+\alpha-\beta)=\frac{1}{\sqrt{3}}$$ then $$\gamma+\alpha-\beta$$ = 30°  ...(3)

Adding we get $$\alpha+\beta+\gamma$$ = 135°  ...(4)

from 1,2,3 and 4 we get $$\alpha$$ = 37.5° therefore answer is option 'A'