This question was uploaded on 05/12/21 on social media accounts.
Solution:
A+B+C = 180 and A,B,C are in AP that means B must be 60.
Let common difference be x:
A = 60-x
C = 60+x
\[\Rightarrow \sin(60-x)\sin(60)\sin(60+x) = \frac{3+\sqrt3}8\]
\[\Rightarrow \sin(60-x)\sin(60+x) = \frac{\sqrt3+1}4\]
\[\Rightarrow \sin^2(60)-\sin^2(x) = \frac{\sqrt3+1}4\]
\[\Rightarrow \sin^2(x) = \frac{2-\sqrt3}4\]
\[\Rightarrow \sin(x) = \frac{\sqrt{2-\sqrt3}}2 = \frac{\sqrt3 - 1}{2\sqrt2}\]
\[\Rightarrow x = 15\]
Now, {A,B,C} = {45,60,75} or {75,60,45}
