If \( \mathrm{AD}, \mathrm{BE} \) and \( \mathrm{CF} \) are the medians of triangle \( \mathrm{A...

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If \( \mathrm{AD}, \mathrm{BE} \) and \( \mathrm{CF} \) are the medians of triangle \( \mathrm{ABC} \), then find the value of \( \frac{1}{4}\left(\mathrm{AB}^{2}+\mathrm{BC}^{2}+\mathrm{CA}^{2}\right)-\frac{1}{3} \) \( \left(\mathrm{AD}^{2}+\mathrm{BE}^{2}+\mathrm{CF}^{2}\right) \)
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