Answer
See explanations.
Work Step by Step
Step 1. Label the apexes with letters $D,E,F,G,H$ as shown in the figure.
Step 2. Identify the given quantities: $DH=2acos\theta-b, EH=a+c, FH=a-c, GH=b$
Step 3. Establish a relation between these quantities via similar triangles $\Delta DEH$ and $\Delta FGH$ to get $\frac{DH}{EH}=\frac{FH}{GH}$ or $\frac{2acos\theta-b}{a+c}=\frac{a-c}{b}$
Step 4. Rearrange the above equation to get $(a+c)(a-c)=b(2acos\theta-b)$ or $a^2-c^2=2ab\cdot cos\theta-b^2$ which lead to the Law of Cosines $c^2=a^2+b^2-2ab\cdot cos\theta$
