For a fixed bit position `b`, determine the conditions under which the bit `b` will be set in the final XOR beauty. Specifically, analyze the parity (odd/even) of the number of triplets `(i, j, k)` where the bit `b` is set in `(nums[i] | nums[j]) & nums[k]`.

Observe that the bit `b` will be set in the final XOR beauty if and only if the number of triplets where the bit `b` is set is odd. Use combinatorial reasoning to count the number of such triplets based on the count of numbers in `nums` that have the bit `b` set (`count_b`) and those that do not (`n - count_b`).

Derive the formula for the parity of the number of triplets where the bit `b` is set. Show that this parity is odd if and only if `count_b` is odd. Conclude that the XOR beauty is simply the XOR of all elements in the array.