Solve p=frac{sigma_{1}+sigma_{2}+sigma_{3}}{3}=frac{sigma_{1}+2sigma_{3}}{3}

$$p = \frac { \sigma _ { 1 } + \sigma _ { 2 } + \sigma _ { 3 } } { 3 } = \frac { \sigma _ { 1 } + 2 \sigma _ { 3 } } { 3 }$$

Evaluate (complex solution)

$$p=\frac{\sigma _{1}+\sigma _{2}+\sigma _{3}}{3}\text{ and }\frac{\sigma _{1}+\sigma _{2}+\sigma _{3}}{3}=\frac{\sigma _{1}+2\sigma _{3}}{3}$$

Solve for σ_3

$$\sigma _{3}=\sigma _{2}$$

$$p=\frac{\sigma _{1}+2\sigma _{2}}{3}$$

Solve for σ_2

$$\sigma _{2}=\sigma _{3}$$

$$p=\frac{\sigma _{1}+2\sigma _{3}}{3}$$