If \( \overrightarrow a = 4\hat i + 2\hat j - \hat k \: and \: \overrightarrow b = 5\hat i + 2\hat j - 3\hat k\), find the angle between \( \overrightarrow a + \overrightarrow b \: and \: \overrightarrow a - \overrightarrow b\).

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