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Verify \( x ^ { 2 } + y ^ { 3 } + z ^ { 3 } - 3 x y z = 1 / 2 ( x + y + z ) \left( ( x - y ) ^ { 2 } + ( y - z ) ^ { 2 } + ( z - x ) ^ { 2 } \right) \) If the bisectors of a pair of corresponding angles so formed by a transversal with twogiven lines are parallel, prove that the given lines are parallel.

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