I'm unsure how to even start this problem
Solve for x:
Arctan( -4/5 ) + Arcos (2/SQRT(5) ) = Arctan(x)
Use your calculator, setting in radians
arctan(-4/5) = -.67474
arcos(2/√5) = .46365
so -.21109 = arctan(x)
x = tan(-.21109) = -.21429
BTW, you will get the same answer if your setting is degrees.
Now take other combinations of ± using the CAST rule
e.g. (setting in degrees)
arctan(-4/5) = 141.34 degrees in quadrant II
arcos(2/√5) = 26.565 in quadrant I
167.905 = arctan(x)
x = tan 167.905 = -.21429