The following formula gives the modified duration:

$$\text{Modified duration} = \frac{\text{Macaulay duration}}{1 + \frac{y}{m}}$$

where $y$ is the yield and $m$ is the compounding frequency per annum.

Macaulay duration is given by:

$$\text{Macaulay Duration} = \frac{\sum (\text{PV of Coupon Payments}) \times T}{\text{Market Price of Bond}}$$

Price of the Bond = $\frac{6}{1.05^1} + \frac{6}{1.05^2} + \frac{106}{1.05^3} = 102.72$

$$\text{Macaulay Duration} = \frac{1}{102.72} \times \frac{6}{1.05^1} + \frac{2}{102.72} \times \frac{6}{1.05^2} + \frac{3}{102.72} \times \frac{106}{1.05^3} = 2.8359$$

Now, the modified duration is

$$\text{Modified Duration} = \frac{2.8359}{1.05} = 2.7009$$

It's worth noting we have rearranged the Macaulay formula so that we have used:

$$\text{Macaulay Duration} = \sum \left[ \frac{\text{PV of Coupon Payments} \times T}{\text{Market Price of Bond}} \right] = \sum \left[ \frac{T}{\text{Market Price of Bond}} \times \text{PV of Coupon Payment} \right]$$