Maclaurin $f(x)=\sin^4x,x\in R$ Write Maclaurin Polynomial$$T\small{10}(x)$$ for function 
$$f(x)=\sin^4x,x\in R$$
Maclaurin Polynomial: 
$$T10(x)=f(0)+f'(0)x+f''(0)\frac{x^2}{2!}+...+f^{10}(0)\frac{x^{10}}{10!}$$
For my problem it means this?
$$f(0)=\sin^40 = 0 $$ 
$$+f'(0)=4\sin^30*\cos0 = 0$$
$$+f''(0)=12\sin^20*\cos0*\cos 0+4\sin^30(-\sin0) = 0+0 =0$$
$$+...$$
Is there any another way how can i get T10 Polynomial?

Hint:
use the $$\sin^2 x=\frac{1-\cos 2x}{2}$$
$$\cos^2 x=\frac{1+\cos 2x}{2}$$
