Location: This mission becomes available after you complete the Chasing the Truth side mission. Wait for an e-mail from Marnie, open it and click on the link inside. This way you will visit the www.epsilonprogam.com. Website again. Click twice on the button of donation of 5000 dollars to the cult's account, to transfer a total of 10 thousand dollars. You now need to wait patiently until there will appear a cult symbol next to Michael's estate, in the Downtown Vinewood district (letter E on the world map). Meet Marnie there (the above screenshot).
After the meeting with Marnie finishes, you should wait for another e-mail and click onto the link in the message. After you gain access to the www.epsilonprogam.com click on the indicated big button and select the Blue Robes option, which will result in buying a complete cultist uniform. It is worth adding that the uniform costs 25 thousand dollars so, if you do not have that amount of money at your disposal, you need to acquire the funds in some way (e.g. by performing some other missions, wait for the income from the other estates that you own, or steal from armored vans).
Return to Michael's villa and use the bed in the bedroom several times (you do not need to save the game here, although this is entirely possible), thanks to which you will speed up time (each interaction with the bed progresses time by 6 hours). Wait about one day this way, and you should receive an e-mail confirming that your uniform has been delivered. Approach the wardrobe, locate the cloths that you have bought (the above screenshot) and put on the Epsilon Robes.
The next requirement is to wear the robes for, at least, ten days and, just like in the case of the recent acquisition, you can speed up time by interacting with the bed. As you can easily calculate, progressing the ten days will require you to perform 40 such interactions. If you have done everything according to the plan, you will eventually receive an e-mail from Cris with congratulations.
Note - if you have waited for the appropriate number of days and you still have not received the confirmation (from the Epsilon store or from Cris) try leaving the villa or not performing any action for the next dozen, or so seconds after you have left the bed.
Rewards for the completion of the mission: none
Requirements for the completion of the mission in 100%: There are no additional requirements for this mission so, it gets completed in 100% automatically.