Did Maedhros fight in the War of Wrath?

[Anguirel]

After the flight (ha ha) of Elwing, Maedhros was left the most powerful Elven force in Beleriand-not that, by that stage, that's saying all that much. He is, except for Cirdan's survivors, the last bulwark against the inevitable victory of Morgoth.

When Earendil takes to the sky in Vingilot, Maedhros sees the Silmaril:

"Surely that is a Silmaril that now shines in the west?"

Maglor replies: "If it truly be the Silmaril which we saw cast into the sea that rises again by the power of the Valar, then let us be glad; for its glory is now seen by many, and yet is secure from all evil."

So far so good. We are then told that Morgoth wasn't expecting anyone to face his armies in open battle again-i.e., he thought Maedhros had a much too reduced army to attack him, and in this he was probably right.

But when the host of Eonwe, Ingwe and Finarfin arrived out of the West, we do not know whether Maedhros did the right thing, put differences aside, and helped them, as the Three Houses of the Edain did. He certainly didn't hinder them. Could he have kept to one side, ashamed of the Elven blood staining him, and watched the greatest battle in history impotently?

The next we hear of Maedhros and Maglor, they seem to be "alone against the world", yet ready to take on Eonwe's host for the Silmarils. Does this imply that they didn't help the Host of the West? Their army has dispersed too; perhaps their remaining followers largely returned west by the command of the Valar?

So the evidence seems to point to Maedhros and Maglor not helping fight Morgoth. But why didn't they? Surely their Oath dictates that they should? Does shame and injured pride, even fear, hold them back? Or did they take part, but on the understanding that the Silmarils would be given to them afterwards-an agreement Eonwe was not authorised to fulfill? If they did take part, this could explain the sudden loss of their retinue-extremely heavy losses.

Is there any more evidence pointing either way in the Grey Annals, the Shibboleth of Feanor, or something of the sort?