What is maximum rang of projectile motion?

Suppose a projectile is fired from a gun, we know that "g" remains constant and as we use horizontal component of velocity in range sov0 also remains constant. Only sin2θ responsible for change in range. The range will be maximum if sin2θ has its maximum value that is 1.

for maximum range:

sin2θ = 1

2θ = sin-1 (1)

θ = 90/2

θ = 45 (degree)

therefor if projectile is projected with the angle of 45(degree) its range will be maximum.