quantum field theory - Some Majorana fermion identities

I have been struggling with these Majorana fermion identities for quite sometime now. I would be grateful if someone can help me with them.

Let $\lambda$,$\theta$ and $\psi$ be $4$-component Majorana fermions. Then apparently the following are true,

• 
  

  $(\bar{\theta}\gamma_5 \theta)(\bar{\psi}_L\theta)(\bar{\theta}\gamma^\mu \partial_\mu \psi_L) = \frac{1}{4}(\bar{\theta}\gamma_5 \theta)^2 (\bar{\psi}_L\gamma^\mu \partial_\mu \psi_L)$

  
  


• 
  

  $(\bar{\theta}\gamma_5 \theta)(\partial _ \mu \bar{\psi}_L \gamma^\mu \theta)(\bar{\theta}\psi_L) = -\frac{1}{4}(\bar{\theta}\gamma_5 \theta)^2 (\partial_\mu \bar{\psi}_L\gamma^\mu \psi_L)$

  
  



• 
  

  $(\bar{\theta}\gamma _5 \gamma _\mu \theta)(\bar{\psi}_L\theta)(\bar{\theta}\psi_L) = \frac{1}{4} (\bar{\theta}\gamma _5 \theta)^2 (\bar{\psi}\gamma ^\mu \psi)$

  
  


• 
  

  $(\bar{\theta}\gamma_5 \theta)(\bar{\psi}_L\theta)(\bar{\theta}\lambda) = \frac{1}{4} (\bar{\theta}\gamma _5 \theta)^2 (\bar{\psi}_L\lambda)$

  
  

I guess looking at the above that all the 4 have some generic pattern and hence probably require some same key idea which I am missing. Its not clear to me as to how to "pull out" the $\theta$s between the other fermions to outside and then again repack then into a $(\bar{\theta}\gamma_5 \theta)$. I will be happy to get some help regarding the above.