Solve to find A:
$2 sin A cos A - cos A - 2 sin A + 1 = 0$

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Solution

$2 sin A cos A - cos A - 2 sin A + 1 = 0$
$2 sin A (cos A - 1) - 1 (cos A + 1) = 0$
$(2 sin A - 1) (cos A - 1) = 0$
$sin A = \frac{1}{2}$ or $cos A = 1$
$sin A = sin 30$ or $cos A = cos 0$
$A = 30^{\circ}$ or $A = 0^{\circ}$
Thus, $A = 30^{\circ}, 0^{\circ}$

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