Embedded Tomcat 7 does not found ServletContainerInitializer from servlet-api 3.x - unit-testing

Question

I'm using the embedded Tomcat 7.0.40 for my unit tests. My webapp uses Servlet 3.x (with x>0).
I managed to deploy my webapp on the Tomcat.
// create the embedded Tomcat
Tomcat tomcat = new Tomcat();
// (...)
// deploy the WAR in the webApp folder
// (...)
// add the WebApp in Tomcat
Context context = tomcat.addWebapp(tomcat.getHost(), "/myapp", webApp.getAbsolutePath());
// (...)
// start the embedded Tomcat
tomcat.start()
However, when I start Tomcat an exception is thrown:
(...)
Caused by: java.lang.NoClassDefFoundError: javax/servlet/ServletContainerInitializer
at java.lang.ClassLoader.defineClass1(Native Method)
at java.lang.ClassLoader.defineClass(ClassLoader.java:791)
at java.security.SecureClassLoader.defineClass(SecureClassLoader.java:142)
at org.apache.catalina.loader.WebappClassLoader.findClassInternal(WebappClassLoader.java:2895)
at org.apache.catalina.loader.WebappClassLoader.findClass(WebappClassLoader.java:1173)
at org.apache.catalina.loader.WebappClassLoader.loadClass(WebappClassLoader.java:1681)
at org.apache.catalina.loader.WebappClassLoader.loadClass(WebappClassLoader.java:1559)
at java.lang.Class.forName0(Native Method)
at java.lang.Class.forName(Class.java:264)
at org.apache.catalina.startup.ContextConfig.getServletContainerInitializer(ContextConfig.java:1659)
at org.apache.catalina.startup.ContextConfig.processServletContainerInitializers(ContextConfig.java:1569)
at org.apache.catalina.startup.ContextConfig.webConfig(ContextConfig.java:1277)
at org.apache.catalina.startup.ContextConfig.configureStart(ContextConfig.java:878)
at org.apache.catalina.startup.ContextConfig.lifecycleEvent(ContextConfig.java:369)
at org.apache.catalina.util.LifecycleSupport.fireLifecycleEvent(LifecycleSupport.java:119)
at org.apache.catalina.util.LifecycleBase.fireLifecycleEvent(LifecycleBase.java:90)
at org.apache.catalina.core.StandardContext.startInternal(StandardContext.java:5269)
at org.apache.catalina.util.LifecycleBase.start(LifecycleBase.java:150)
... 7 more
Caused by: java.lang.ClassNotFoundException: javax.servlet.ServletContainerInitializer
at org.apache.catalina.loader.WebappClassLoader.loadClass(WebappClassLoader.java:1714)
at org.apache.catalina.loader.WebappClassLoader.loadClass(WebappClassLoader.java:1559)
... 25 more
The javax.servlet.ServletContainerInitializer is localized in the javax.servlet-api JAR starting from version 3.1.
Do you know how to solve this issue?
How can I add programatically this library in the classpath of the embedded Tomcat?
I try several methods by none work...
Thanks for help.