Thermodynamics

I'm stuck on a question on a thermo sheet and it is

A possible ideal-gas cycle operates as follows:
(i) From an initial state (p1; V1) the gas is cooled at constant pressure to (p1; V2);
(ii) The gas is heated at constant volume to (p2; V2);
(iii) The gas expands adiabatically back to (p1; V1).
Assuming constant heat capacities, show that the thermal efficiency is

1-(gamma)*((V1/V2)-1)/((P2/P1)-1)

what I currently have is

for the Isobaric part:
dW=P1(V2-V1) and dQ=Cp(T2-T1)

The const vol part:
dW=0 and dQ=Cv(T2-T1)

The adiabatic part
dW=(P2V2-P1V1)/(gamma-1) and dQ=0

where gamma=Cp/Cv

Any help would be much appreciated

thanks

Thermal efficiency is defined as $\eta = \dfrac{W_{\text{out}}}{Q_{\text{in}}}$. By energy conservation, $Q_{\text{in}} = Q_{\text{out}} + W_{\text{out}} \implies \eta = 1 - \dfrac{Q_{\text{out}}}{Q_{\text{in}}}$.

For (i), the heat transfer to the environment by the gas cooling is $Q_{\text{out}} = \int_{T_1}^{T_2} C_P \ \text{d}T = C_P (T_2 - T_1)$

For (ii), the heat transferred to the gas ($Q_{\text{in}}$) is $Q_{\text{in}} = \int_{T_2}^{T_3} C_V \ \text{d}T = C_V (T_3 - T_2)$

For (iii), $Q = 0$ as it is an adiabatic process.

With $PV/T = \text{constant}$ and some algebraic manipulation, the result should fall out.