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In a triangleABC, if |[1,1,1][1+sinA,1+s...

In a `triangleABC`, if `|[1,1,1][1+sinA,1+sinB,1+sinC],[sinA+sin^2A,sinB+sin^2B,sinC+sin^2C]|=0`, then prove that `triangleABC` is an isosceles triangle.

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$$ \Delta=\left|\begin{array}{ccc} 1 & 1 & 1 \\ 1+\sin A & 1+\sin B & 1+\sin C \\ \sin A+\sin ^{2} A & \sin B+\sin ^{2} B & \sin C+\sin ^{2} C \end{array}\right| $$ $$ ...
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