Vector f has a direction angle a= 45 (degrees) it is known that cos b is twive as large as cos y find angles b and y (a= alpha b=beta, y= gama)

i want to know if i did this equation right

i know that cosb = 2cosy

and i have the formula cos a^2 + cos b^2 + cos y^2=1

so i plug in cosb=2cosy in for cosb^2

and i get : cos45^2 + 2cosy^2 + cosy^2 = 1

then: .5+ 3cosy^2=1

3cosy^2= .5

y= 65.9 deg

then plug it back in to original

so: cos45^2+cosb^2+cos 65.9^2=1

then you get cosb^2=.333

cosb=sqrt(.333)

b=Cos^-1(.333)

b=54.74deg

thanks for the help