A rod of mass \(\displaystyle{M}\) and length \(\displaystyle{2a}\) is placed horizontally on the edge of a table. Initially, the centre of mass of the rod is at a distance of \(\displaystyle{^a/_3}\) from the edge. The rod is released from the rest. The rod slips after it has turned through an angle \(\displaystyle{ \theta }\).
The coefficient of friction \(\displaystyle{\mu}\) between the rod and the table can be expressed as \[\dfrac{a}{b} \tan \theta.\] Find \(\displaystyle{a+b.}\)

**Note**

- \( a \) and \( b\) are positive, co-prime integers.
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