Question

Sin4a+cos2a+cos2asin2a

Answer 1

Sin4a+cos2a+cos2asin2a=sin4a+cos2a(1+sin2a)=sin4a+cos2a(sina+cosa)^=sin4a+cos2a=2sin2acos2a+cos2a=cos2a(2sina+1)=0
cos2a=0
2a=pi/2+pi n
a=pi/4+pi n/2

2sina+1=0
sina=-1/2
a=(-1)^n+1*pi/6