Why are my quotation marks causing an “unexpected token” error with this command?

I need help with a specific command that I am using in a new game that I am creating inside of Minecraft. The command I have so far is:

/give @p sign 1 0 {BlockEntityTag:{Text1:"{"text":"
[MF2]","color":"gold","clickEvent":
{"action":"run_command","value":"tellraw @a ["",{"text":"[MF2] 
","color":"gold"},{"selector":"@p","color":"dark_aqua"},{"text":" is now an
admin of the server!","color":"white"}]"}}",Text3:"{"text":"Click to join
Admin","color":"dark_aqua","clickEvent":
{"action":"run_command","value":"scoreboard teams join admin @p"}}"},display:
{Name:"Custom Sign"}}

If I take out the /tellraw command, the command works fine, but I need the inner command to announce to the game that a new admin has joined.

With /tellraw inside, the error message reads:

Data tag parsing failed: Unexpected token t at:

text":"[MF2]","color":"gold","clickEvent":{"action":"run_command","value":"tellraw
  @a [""{"text":"[MF2] ","color":"gold"},
  {"selector":"@p","color":"dark_aqua"},{"text":" is now an admin 
  of the server!","color":"white"}]"}}",Text3:"{"text":"Click to join
  Admin","color":"dark_aqua","clickEvent":
  {"action":"run_command","value":"scoreboard teams join admin @p"}}"

If anyone knows how to fix this, please let me know.

Related:

• Escaping inside of an already-escaped string