Did Hagoromo have the Mangekyo Sharingan?

My theory would be that the Rinnegan is directly related to the Sharingan but different dojutsu. The Rinnegan shown by Kaguya with the tomoe's is the simultaneous realise of both the Rinnegan and Sharingan, that's if we assume she was in possession of all the 3 great dojutsu. Next in line would be her sons Hagoromo and his brother. We know his brother received the Byakugan, simple, the issue lies in why does his brothers Rinnegan differ from his mothers if we accept that he received this. One assumption could be that after becoming the Shinjus Jinchuriki he received the Rinnegan, as he would now be in possession of his mothers chakra, but this is stretch with little evidence especially if we consider the fact that Madara received his Rinnegan after he had both Senju and Uchiha chakra.

A more plausible theory could be that the Sharingan can be activated simultaneously with the Rinnegan. This could explain the tomoes possessed by Sasuke and Kaguya/Shinju (in Sasukes case he already had the Sharingan by receiving chakra/eyes of the Sage he now possess the criteria to activate them simultaneously. The difference in tomoe between him and Kaguya could be due to her vast chakra/direct link to the Shinju/being the progenitor, considering the Sage had become the Shinju's Jinchuriki it would interesting to see if he was in possession of a Rinnegan similar to his mother, why I say this is explained further below).

It could be plausible that the Rinnegan without the Sharingan could be the Sharingan at rest. Further to this I propose that the Sharingan and the Rinnegan are separate dojutsu yet have a symbiotic relationship I say this simply because of Nagato. Yes the eyes were transplanted but they would of possessed the same power as Madara, therefore it wouldn't be to ridiculous to assume he would have the Sharingan as well, but there is no evidence of this, instead he is only shown using the Rinnegan, suggesting he only received that one dojutsu. Also to re-illiterate a previous point, as seen by Nagato, after he activated his Rinnegan he was able to keep it activated continuously, which may suggest it expends minimal chakra, so it may not be hard to believe that the Sages Rinnegans appearance may be just his Sharingan deactivated.

To review, so far I have theorised that the Sharingan and the Rinnegan are two separate dojutsu with a symbiotic relationship of some sort. What can be said is that awakening the Rinnegan requires both Senju and Uchiha DNA, so both the eyes of the Sage and body essentially. Meaning the Sharingan is required to evolve to activate the Rinnegan. Considering all this you can assume that the Sage was in possession of the Sharingan and it is likely that we have yet to see him activate them simultaneously. Further again, when he had his two sons his eyes and body were split, therefore the critera for the activation of the Rinnegan was lost, but to say it was "his" eyes would suggest he was in possession of the Sharingan to begin with.

Overall the Sharingan and the Rinnegan are two separate doujutsu with an intrinsic relationship, the eyes shown by Kaguya/Shinju and Sasuke would be the activation of both dojutsu simultaneously in their eyes, which would prose that the Sage either has the potential to use the Sharingan or we are to see him use it in unison with his Rinnegan.
Obviously this is all just speculation from what I've seen! Guess we'll just have to wait and see!